# Efficient Implementation of Polymer Microwave Fiber Links Employing Non-Galvanic Coupling Mechanism
## 3 PMF-AiP Coupling
### Coupler Design  
The proposed solution for the coupling mechanism is based on the lateral coupling of the signal from the MMIC to the PMF. Multiple antenna structures are capable of lateral radiation, such as the bowtie antenna, the dipole antenna and more [4]. However, the application at hand requires high directivity in the lateral direction to minimize the coupling losses. The Vivaldi antenna is an ideal solution for this application. In principle, a Vivaldi antenna design requires multiple redistribution layers. However, in our work, a single-layer Vivaldi antenna is proposed, achieving lower manufacturing costs and complexity. More specifically, the proposed antenna is a variation of the antipodal Vivaldi antenna [12; 30], which utilizes three metal layers. However, the proposed design is implemented in the single redistribution layer of the eWLB stack-up. This implementation implies that the input of the antenna is differential (Figure 10), in contrast to a multiple-metal-layer process, where the input of the antenna can be single-ended. Our antenna can be decomposed into three parts, namely the differential coplanar strip line (DCPS), the antenna body and the wave magnifier, which, in our proposed design, is an elliptic metal layer (Figure 10), although alternative shapes are also possible. Figure 9: Simulation results in terms of the \(|\)S21\(|\) of a dual CPS for three eWLB modeling cases. The DCPS connects the Vivaldi slot to the IC and is matched at 100 Ohms differential impedance to ensure maximum power transfer. The thickness of each trace is standard and is predefined by the technology. The width of each trace, \(W_{t}\), and the gap, \(W_{gap}\), between the two traces affect the differential impedance of the strip line and its insertion losses. The antenna body is composed of two RDL traces, as shown in Figure 10, with total length \(L\). The total width of the Vivaldi slot is \(W\) and the length of the edge is \(d\). By defining these three geometric parameters and taking into consideration that the gap between the two traces of the Vivaldi slot must be the same as the DCPS at the point where they are connected, we can define the curved edges of the two traces [4]:  
\[ \begin{array}{c}C_{1}\left(t\right)=\pm 0.5*W_{\text{gap}}*exp(r_{1}\ t),\ 0\leq t\leq L\\ C_{2}\left(t\right)=\pm\left(0.5*W_{\text{gap}}+W_{\text{t}}\ \right)*\exp(r_{2}\ t)\\ 0\leq t\leq L-d,\end{array}  \tag{4}\]  
where \(r_{1}\) and \(r_{2}\) are defined by the conditions \(C_{1}(L)=W\) and \(C_{2}(L-d)=W\). The role of the Vivaldi slot is to guide the incident wave from the DCPS to radiate laterally with the minimum possible scattering losses, which is not possible using a simple slot. Finally, concerning the magnifier, its general shape is not important, although its dimensions and its position with respect to the antenna body are. By appropriately adjusting the geometric parameters of the magnifier, we can boost the radiating field in the desired direction. The magnetic field of the wave creates a secondary current source on the magnifier, which acts as a secondary radiator. The superposition of the primary and secondary waves increases the gain of the antenna. In Figure 11, the Poynting vector at the edge of the antenna with and without the magnifier is shown, illustrating the amplification of the electromagnetic field of the antenna with the magnifier. Figure 12 shows the 3D electric field distribution of the antenna with and without the magnifier, where we can clearly see the field intensity difference. The position and dimensions of the magnifier have an impact on the antenna's performance. We ran parametric simulations in HFSS to determine the optimal \(D_{\text{m}}\) and \(R\) parameters (Figure 10), while keeping the \(R/r\) ratio  
Figure 10: Single-layer antenna geometry. constant. The final decision for the magnifier was based on the result with the highest gain, without the presence of the PMF, since the results are transferable. In Figure 13, the normalized E- and H-field patterns in dB are shown at 140 GHz.