# Folded Heterogeneous Silicon and Lithium Niobate Mach-Zehnder Modulators with Low Drive Voltage
## 3 Results and Discussions  
To validate the folded MZM design, we fabricated and measured folded devices with a total modulation length of 12 mm (Figure 1f). For comparison, the non-folded counterpart was also fabricated on the same wafer. Due to the two U-turns, the length of the folded device is reduced to approximately two-fifths that of the non-folded device, which is about 5.6 mm. We first employed the 100 kHz triangular voltage sweep method to characterize the V\({}_{\pi}\) for both devices. The V\({}_{\pi}\) values for the folded and non-folded devices are 2.16 V and 2.25 V, corresponding to voltage-length products of 2.6 V\(\cdot\)cm and 2.7 V\(\cdot\)cm, respectively. The slightly lower V\({}_{\pi}\) value for the folded device is because of the additional phase modulation in VACs at both ends of the optical U-turn waveguides. The inset of Figure 2a shows the transmission of the folded device, demonstrating a measured extinction ratio of \(>\)35 dB. Next, we characterized the EO bandwidth (S\({}_{21}\) parameter) for three types of devices: (1) non-folded device, (2) folded device with velocity-matched microwave delay lines (L\({}_{\text{D}}\) = 313 \(\upmu\)m), and (3) folded device without microwave delay lines (L\({}_{\text{D}}\) = 0), as depicted in Figure 2b. The measured modulation bandwidth of the folded and non-folded MZM is 50 GHz and 60 GHz (with a reference frequency of 2 GHz), respectively. The bandwidth of the folded device with velocity-matched microwave delay lines is slightly smaller than the non-folded device because the TWE in the folded device possesses extra microwave loss due to the additional U-turns. In contrast, bandwidth of the folded device without microwave delay lines is significantly smaller than the other cases. These results show that compensating for the optical wave and microwave time delay is essential to achieve large bandwidths in folded MZMs. To further reduce the V\({}_{\pi}\), we fabricated folded devices with a total modulation length of 21 mm, whose actual device length is 8.7 mm. As shown in Figure 2c,d, the measured V\({}_{\pi}\) and bandwidth for such a device is 1.24 V and 40 GHz, respectively, which are very well facilitated for high-speed and low-drive-voltage operation. The RF return losses (S\({}_{11}\) parameter) of the devices are less than--15 dB at up to 67 GHz, indicating that the microwave U-turns do not introduce significant impedance discontinuities in TWE. The device also features a low on-chip loss of 2.9 dB. The high-speed modulation ability of the modulator has also been characterized. First, we use the 12 mm device to demonstrate high-speed data modulation. Figure 3a,b show the optical eye diagrams for OOK modulation at 80 Gb s\({}^{-1}\) and 100 Gb s\({}^{-1}\). The measured extinction ratios are 7.8 and 5.8 dB, respectively. We also performed the PAM-4 modulation experiments at 56 Gbaud (112 Gb s\({}^{-1}\)) and 64 Gbaud (128 Gb s\({}^{-1}\)); the results are shown in Figure 3c,d. Figure 3e shows the back to back (B2B) bit-error rate (BER) versus the received optical power for 112 Gb s\({}^{-1}\) and 128 Gb s\({}^{-1}\) PAM-4 signal transmission. The details of the B2B BER measurements can be found in our previous work [20]. In addition to the data rate difference, the 1.5 dB power penalty between the 56 Gbaud and 64 Gbaud is partly due to the bandwidth constraint of the oscilloscope. Furthermore, we employ a CMOS digital-to-analog converter (DAC) circuit to generate 32 Gbps electrical OOK signals with peak-to-peak voltage of 350 mV, which was used to directly drive the fabricated low-V\({}_{\pi}\) modulator with the total modulation length of 21 mm. Figure 3f shows the optical eye diagram with measured extinction ratio of 2.7 dB. We also performed higher data rate experiments up to 112 Gb s\({}^{-1}\) with an RF amplifier on this device; the results can be found in the Supplementary Materials, Section S4.