# Folded Heterogeneous Silicon and Lithium Niobate Mach-Zehnder Modulators with Low Drive Voltage
## 1 Introduction  
By harnessing the mature CMOS foundries, silicon photonics based on silicon-on-insulator (SOI) platforms promises the low cost and high volume production for photonic integrated circuits (PICs) [1; 2]. This makes it a leading technology for future optical transceivers in both short-reach and long-haul optical communication links, in which high-speed, low-drive-voltage, and low-loss modulators are crucial components [3; 4]. Conventional silicon optical modulators rely mainly on the free-carrier effect in silicon p-n junctions. Unfortunately, the free-carrier effect has intrinsic limitations in modulation bandwidth, optical loss and nonlinear response [5; 6; 7; 8; 9]. Indeed, the current performance metrics of the silicon optical modulator are more or less close to its physical limits, but future applications require even higher performance due to the insatiable demands of ever-increasing data capacity.  
Tremendous efforts have been made toward heterogeneously integrating materials with strong electro-optic effects onto the silicon photonics platform, including graphene [10], electro-optic (EO) polymers [11], indium phosphide (InP) [12], and barium titanate (BTO) [13]. In addition to these materials, lithium niobate (LN), the most successful material for EO modulation [14; 15; 16], has also been integrated with silicon photonic circuits by using die-to-wafer bonding technique [17; 18; 19; 20]. To date, the heterogeneous LN/SOI Mach-Zehnder modulators (MZMs) have exhibit very appealing overall performance in terms of half-wave voltage (V\({}_{\pi}\)), modulation bandwidth, and optical loss. However, the length of the Si/LN MZM is relatively long for low-drive-voltage operation, due to the moderate modulation efficiency (V\({}_{\pi}\)L). The \"holy grail\" of the optical modulator research is a fast and low-loss device with a V\({}_{\pi}\) of about 1 V, which would make it possible to drive the devicedirectly by CMOS electronic circuits and would significantly reduce the cost and power consumption of optical transceivers. For Si/LN MZM, the modulation efficiency is about 2-3 V\(\cdot\)cm. Therefore, the device length needs to be 20 mm or more to obtain a V\({}_{\pi}\) of about 1 V. Such a slender structure brings inconvenience to integration with other devices to form sophisticated photonic integrated circuits, and it is difficult to adapt to a compact transceiver package, such as QSFP-DD (quad small form factor pluggable double density).  
Here, we report a folded Si/LN traveling wave MZM, in which the optical arms of MZM and traveling wave electrode (TWE) each undergo two 180-degree U-turns, thereby reducing the length of the phase modulation region by nearly 60%. Moreover, by matching the time delays of the optical and microwave U-turns, a perfect velocity match between the optical wave and the modulating microwave can be achieved over the entire modulation section, leading to a large modulation bandwidth. For a folded Si/LN MZM with device length of less than 9 mm, we measure a V\({}_{\pi}\) as low as 1.24 V. Such a device can be driven directly by low-cost and energy-efficient CMOS electronic circuits. In addition, the present device shows a low on-chip insertion loss of <3 dB and large extinction ratio of >35 dB. On-off keying (OOK) modulation up to 100 Gbit/s and PAM-4 modulation up to 128 Gbit/s are successfully demonstrated.