# Folded Heterogeneous Silicon and Lithium Niobate Mach-Zehnder Modulators with Low Drive Voltage
## 2 Materials and Methods  
Figure 1a shows the schematics of the present folded Si/LN MZM. The device consists of an SOI substrate (220 nm silicon, 3 \(\upmu\)m buried oxide layer) with a 600 nm thick layer of X-cut LN membranes on top fabricated based on benzocyclobuten (BCB) adhesive die-to-wafer bonding technology. The top layer is an array of LN waveguides for pure phase modulation (through the Pockels effect). The bottom silicon photonic waveguide supports all the other passive functions, consisting of grating couplers for off-chip coupling, 3 dB multimode interference (MMI) couplers that split and combine the optical power, as well as bent and cross waveguides for folding the optical structure. Optical wave couples up and down between the two layers via vertical adiabatic couplers (VACs), formed by silicon inverse tapers and overlapping LN waveguides. The meandering arms of the MZM consist of three parallel straight phase modulation sections interconnected by two optical and microwave U-turns. The straight phase modulation section is composed of a pair of LN waveguides running through the gaps of the ground-signal-ground (GSG) TWE (Figure 1b), which operates in a single-drive push-pull configuration. As a result, the applied microwave fields induce a positive phase shift in one LN waveguide and a negative phase shift in the other, leading to nearly chirp-free modulation. The optical waves are coupled from one phase modulation section to another, by passing successively through a pair of VACs, a pair of mutually crossed silicon U-turn waveguides, and another pair of VACs. Here, the two silicon U-turn waveguides were deliberately designed to be mutually crossed. This is because the direction of the electric field is flipped after folding the TWE. To avoid the phase difference in the LN arms being cancelled out before and after the U-turn, the silicon waveguides need to be crossed to ensure that phase differences continue to accumulate. All silicon U-turn waveguides are located at the bottom of Au electrodes, and the interlayers consist of BCB (300 nm) and LN (600 nm), which can promise a negligible absorption loss of silicon waveguide. We elaborate the design of the U-turns in both optical waveguides and TWE, which are the most critical part of the device and have to be carefully designed in order to provide velocity matching and to minimize extra microwave and optical losses. The detailed designs of the other parts, including a straight LN waveguide, straight TWE, 3 dB MML, and VACs, can be found in Ref [19]. As shown in Figure 1d, the silicon U-turn optical waveguides consist of three parts. The first part is a 135-degree Euler bend with a minimum curvature radius of 28 \(\mu\)m. The second part is a waveguide cross [21] with a low insertion loss of \(<\)0.15 dB and low crosstalk of \(<-40\) dB (Supplementary Materials, Section S1). The third part is a 45-degree Euler bend with a minimum curvature radius of 15 \(\mu\)m. Due to the high index contrast of the silicon waveguide, the minimum curvature radius for Euler bends can be less than 5 \(\mu\)m. The reason we choose moderate radius values here is to ensure that the middle ground is wide enough to avoid unwanted microwave crosstalk (Supplementary Materials, Section S2). In this work, the widths of the signal and ground electrodes are set to 17 \(\mu\)m and 120 \(\mu\)m, while the thickness and gap are set to 800 nm and 7.3 \(\mu\)m, respectively, to achieve good impedance and optical-microwave velocity matches in the modulation region. The TWE U-turn consists of two microwave delay lines and a 180-degree circular bent TWE, as shown in Figure 1a. The radius of the circular bent TWE is 75.8 \(\mu\)m measured at the center of the S electrode. The simulation results indicate that such a bent electrode features a low microwave loss and shows a low microwave reflection at the interface between the bent and straight electrodes (Supplementary Materials, Section S2).