## 2 Design  
The electro-optic modulator uses a coplanar waveguide (CPW) traveling wave electrode design in the push-pull configuration on the x-cut TFLN platform. Based on the market specifications of available lithium niobate on insulator (LNOI) wafers, a substrate with a buried oxide layer (SiO\({}_{2}\)) thickness of 4.7 \(\upmu\)m is selected. Directly etched lithium niobate (LN) ribs on the LN layer are used for light propagation, and the RF field is applied via gold electrodes deposited on a SiO\({}_{2}\) buffer layer, such that the applied field aligns along the z-axis to utilize the strongest Pockel's coefficient \((r_{33}=30\) pm/V). A cladding is provided to guard the device against environmental damage and support microvia connectors [14; 24]. Figure 1 shows the cross-section and the top view of the device, and Table 1 enlists the different dimensions displayed in the figure. Parameters deciding the performance metric of the electro-optic modulator depend on the regular coplanar waveguide line's characteristic impedance, effective indices and RF losses, which are decided by dimensions listed in Table 1. Among these dimensions, BOX thickness, and silicon layer thickness are fixed by the manufacturer (in our case). Dimension of rib and the LN layer are decided to obtain single mode operation and electrode thickness is fixed at 0.5 \(\upmu\)m. Buffer thickness is kept at 0.2 \(\upmu\)m, as a thicker buffer will affect the electrtic field distribution and a thinner buffer layer leads to increase in metal-induced optical losses. Thus, we are left with \(\text{h}_{\text{clad}}\), trace width (\(\text{w}_{\text{c}}\)), electrode gap (\(\text{w}_{\text{g}}\)), rib distance (D) and electrode thickness (\(\text{t}_{\text{Au}}\)). These parameters should be optimized for a high bandwidth operation at a low half-wave voltage (\(V_{\pi}\)) to achieve maximum velocity matching (\(\Delta\)m = n\({}_{\text{eff}}\)-n\({}_{\text{op}}\)), impedance matching (R = (Z\({}_{\text{in}}\)-Z\({}_{\text{L}}\))/(Z\({}_{\text{in}}\) + Z\({}_{\text{L}}\))) and low microwave losses. Here n\({}_{\text{eff}}\), \(Z_{\text{in}}\) and n\({}_{\text{op}}\) are the effective RF refractive index, input line impedance and optical group index, respectively. Microwave losses are governed by three types of losses in CPW traveling wave electrodes: conductor losses, dielectric losses and radiation losses [12; 25; 26]. Conductor losses are decided by skin depth and vary as a square root function of frequency; dielectric losses are calculated using loss tangent and vary as a linear function of frequency. Radiation losses depend on the surface roughness of the metal electrodes. Optimized fabrication techniques allow the RMS surface roughness value to be constrained within a few nanometers [27; 28]; thus, the effects of surface roughness are neglected in device modeling considering the plain electrode deposition [12; 21; 22]. At an RF frequency of 100 GHz, \(\text{w}_{\text{c}}\) and \(\text{w}_{\text{g}}\) are varied for different h\({}_{\text{clad}}\) to study the variation in n\({}_{\text{eff}}\), Z\({}_{\text{o}}\) and RF losses of CPW using COMSOL multiphysics solver. Equivalent optical mode group index for different values of h\({}_{\text{clad}}\) were obtained. After a critical optimization, h\({}_{\text{clad}}\) was decided to be 2.75 \(\upmu\)m, and corresponding results are shown in Figure 2. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \(t_{LIN}\) & \(h_{rib}\) & \(w_{rib}\) & \(t_{Buffer}\) & \(t_{Au}\) & \(h_{clad}\) & \(h_{BOX}\) & \(h_{Si}\) \\ \hline
0.3 \(\upmu\)m & 0.4 \(\upmu\)m & 1.25 \(\upmu\)m & 0.2 \(\upmu\)m & 0.5 \(\upmu\)m & 2.75 \(\upmu\)m & 4.7 \(\upmu\)m & 500 \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of various layers displayed in Figure 1.  
Figure 1: (**a**) Cross section and (**b**) top view of the proposed electro-optic modulator. An optical mode group index (n\({}_{\rm op}\)) of 2.238 was obtained based on the dimensions used in the simulations.