High-speed electro-optic (EO) modulators play a crucial role in achieving high levels of integration in compact chips, enabling diverse applications, including optical interconnect^[1], microwave photonics^[2], quantum photonics^[3], and optical computing^[4]. Recent strides in technology have led to the development and commercialization of lithium niobate on insulator (LNOI) platforms, giving rise to on-chip integrated lithium niobate modulators. Compared to conventional bulk lithium niobate modulators, these integrated counterparts offer substantial advantages in terms of EO bandwidth, driving voltage, and optical losses while retaining fundamental material benefits, such as a linear EO response, minimal optical losses, and a wide transparent window. During the past few decades, numerous thin-film lithium niobate (TFLN) EO modulators with large EO bandwidth and low drive voltage have been successfully demonstrated^[5–9]. The most remarkable EO bandwidth achieved with TFLN modulators has reached 110 GHz, achieved by utilizing a capacitive-loaded traveling wave electrode and quartz substrates^[10]. The majority of TFLN modulators have been predicated on a conventional Mach–Zehnder interferometer (MZI) configuration. However, due to the constrained material Pockels coefficient of lithium niobate (γ33=30.8), the phase shifter’s length is typically necessitated to be several centimeters^[11]. This intrinsic characteristic presents a notable limitation of TFLN modulators when compared with alternative integration platforms like silicon, indium phosphide, and polymers.

The solution to addressing this challenge is enhancing the EO interaction to improve the modulation efficiency of the lithium niobate modulators. A general approach is to use resonant EO modulator structures, including but not limited to ring modulators^[12–16], photonic crystal modulators^[17], Bragg grating cavity modulators^[18], and Fabry–Perot (FP) cavity modulators^[19,20]. In their most basic form, such modulators allow the resonance frequency to be changed by an applied electrical field. As a result, the transmission of light at a frequency near resonance can be modulated. However, adopting a resonant modulator structure comes at the expense of sacrificing the operating wavelength range. To achieve effective light modulation, the laser source’s wavelength must be precisely aligned near the resonance point. Furthermore, the resonance phenomenon amplifies the modulator’s susceptibility to variations in environmental factors like temperature, imposing stricter requirements on the control of the operating wavelength. Therefore, how to realize TFLN modulators that concurrently possess a compact footprint and a wide wavelength operating bandwidth remains an essential but complex problem.

Here, we theoretically proposed and experimentally demonstrated a TFLN Mach–Zehnder modulator (MZM) with a small footprint and high modulation efficiency using a mode-folded phase shifter without sacrificing the operating wavelength bandwidth. After each pass through the phase shifter, the optical signal is converted into another waveguide mode by a mode converter. Benefitting from the inherent orthogonality of different waveguide modes, the optical signals avoid interfering with each other as they pass through the phase shifter. This property ensures the modulator’s capability to operate across a wide wavelength range while bolstering the modulation efficiency. Meanwhile, the TFLN is intrinsically supportive for high-order mode modulation due to its fully overlapped electric and optic fields in the lithium niobate material and thus easily breaks the limit of PN-junction-dependent modulation for silicon modulators that have already achieved a half-wave voltage length product of only 0.37 V·cm based on a two-mode-looped structure^[21]. Higher-order mode phase modulation on TFLN has already been proved to be an effective approach for increasing the number of the EO modulation optical combs^[22,23]. The device features a footprint of 2.7mm×0.6mm and exhibits a high modulation efficiency among the reported TFLN MZM results, corresponding to a low half-wave voltage length product of 1 V·cm. Experimentally, we obtained a proof-of-concept 3-dB electro-optic bandwidth of 12 GHz. These outcomes yield fresh perspectives on the feasibility of implementing TFLN MZMs with a compact footprint.

The schematic structure of the proposed MZM is shown in Fig. 1(a), which consists of two 3-dB power splitters, eight mode converters, and two multimode phase shifters, supporting the TE0, TE1, and TE2 modes. The working principle of the proposed modulator can be described as follows. The input light is initially divided into two separate paths by the 3-dB power splitter, traversing the multimode phase shifter in the TE0 mode. Following modulation through an external electric field, the optical signal in the TE0 mode is transformed into the TE1 mode using a mode converter. It subsequently undergoes a second pass through the phase shifter before returning to the starting point of the phase shifter. At this juncture, the optical signal in the TE1 mode is transformed into the TE2 mode via two additional mode converters situated at the onset of the phase shifter. The signal then proceeds through the phase shifter for the third time, effecting phase modulation. Ultimately, the TE2 mode is reconverted to the TE0 mode utilizing another mode converter. The final step involves the interference of the TE0 mode with the other branch of light at the power combiner. Overall, the optical signal undergoes phase modulation through the phase shifter three times, sequentially in the TE0, TE1, and TE2 modes. The cumulative phase alteration result is the summation of the individual phase changes in these three distinct waveguide modes. Consequently, the modulator is expected to achieve a threefold enhancement in modulation efficiency within the same phase shifter length.

The mode converter plays a critical role in achieving the comprehensive functionality of the entire device. Here, a tapered asymmetric directional coupler (ADC) structure is utilized, which features low insertion loss, broadband operation, and high fabrication tolerance. A 0.5-mm-long lumped ground-signal-ground (GSG) electrode was employed for high-speed modulation. The entire device structure was designed and fabricated on a commercial x-cut LNOI wafer with a 600-nm x-cut lithium niobate (LN) layer and a 4.7-μm-thick buried oxide layer on a silicon substrate. The fabrication process of the device started with the LN waveguide structure patterning using electron-beam lithography. The LN waveguide was partly etched by the dry etching process. The LN etching depth was 300 nm, leaving a 300 nm slab. A 250-nm-thick Au layer was deposited using electro-beam evaporation and patterned by lift-off processes. The width of the single-mode waveguide throughout the device was established at 800 nm, whereas the width of the multimode waveguide within the phase shifter segment was configured to 5.66 µm. The gaps between the signal and ground electrodes were set to 15.66 µm due to the limited alignment accuracy of the UV lithography. The microscope images of the fabricated device are shown in Fig. 1(b). Figures 1(c)–1(e) depict detailed scanning electron microscope (SEM) images focusing on the coupling region of the ADC, the multimode interferometer (MMI), and the electrode gap.

The static transmission spectrum of the fabricated modulator was first measured using a tunable laser source (Santec TSL-710) and a power monitor. The tunable laser source was coupled to the device under test (DUT) using a lensed fiber aligned to launch TE-polarized light. The measurement result is shown in Fig. 2. The fiber-to-fiber insertion loss at the peak transmission level is measured to be 28 dB, primarily stemming from the unpolished end face of the waveguide. The coupling loss between the single-mode LN waveguide and the lensed fiber is measured to be 20 dB through a reference waveguide structure. Therefore, the on-chip loss for the proposed device is determined to be 8 dB. The coupling loss can be further improved using edge-coupled spot-size converters.

As is shown in Fig. 2(a), the static transmission spectrum of the fabricated device can be regarded as a combination of the transmission spectrum of an unbalanced MZI superimposed with an interference spectrum with a smaller free spectral range (FSR). The zoom-in view of the transmission spectrum is shown in Fig. 2(b). The MZI envelope exhibits an extinction ratio of 14 dB, coupled with a 10-nm FSR. The interference spectrum overlaid on the MZI envelope exhibits an extinction ratio of 6 dB, with an FSR of 0.2 nm. Through theoretical analysis, it has been discerned that the superimposed interference spectrum arises due to mode crosstalk introduced by the TE0–TE2 mode converter. Notably, when the mode crosstalk created by the mode converter remains below −20dB, the extinction ratio of the superimposed interference spectrum becomes insignificantly small, rendering it practically negligible.

The modulation efficiency of the proposed device was further measured by applying a 100-kHz triangular wave with an amplitude of 40 V. The measurement result is shown in Fig. 3(a). The half-wave voltage of the device is determined as 20 V. Considering the length of the phase shifter, 0.5 mm, the VπL of the proposed device is calculated to be 1 V·cm. To validate the modulation efficiency enhancement, we fabricated a conventional MZM with a 2-mm phase shifter length on the same chip. The conventional MZM has the same electrode structure as the proposed device. The distinction between the two devices is attributed to variations in the width and length of the waveguide in the phase shifter section. The waveguide width of the conventional MZM is set to 800 nm so that it can support a single transverse-electric (TE) polarized fundamental mode. We applied the same triangular wave signal to the conventional MZM, and the measured light transmission is shown in Fig. 3(b). The half-wave voltage of the conventional MZM is determined as 18.6 V, corresponding to a VπL of 3.7 V·cm. From the results of the comparative experiment, the modulation efficiency of the proposed device has been enhanced by a factor of 3.7 compared to the conventional MZM.

In our design, three waveguide modes were used to recycle in the multimode phase shifter, while we observed an over-three-times modulation efficiency enhancement. To confirm this better-than-expected behavior, we performed a simulation using COMSOL Multiphysics to calculate the mode effective index variation of different modes in the LN rib waveguide. In the simulation, the widths of the single-mode waveguide and multimode waveguide are set to 800 nm and 5.66 µm, respectively, consistent with the waveguide width in the fabricated device. The calculated result is shown in Fig. 4(a). From the results, it can be observed that under identical applied voltage and electrode gap conditions, the mode effective index variation for each mode within the multimode waveguide surpasses that of the TE0 mode within the single-mode waveguide, corresponding to a higher phase modulation efficiency. Specifically, the modulation efficiency enhancement factors for the TE0, TE1, and TE2 modes in the multimode waveguide are calculated to be 1.21, 1.21, and 1.25, respectively. Consequently, the overall modulation efficiency enhancement factor is the summation of the enhancement factors for the three waveguide modes, resulting in a calculated value of 3.67.

The greater effective index variation of the optical modes in the multimode waveguides is mainly attributed to the increased lateral optical confinement of the multimode waveguide. To quantify this optical confinement discrepancy across various waveguide modes, a confinement factor was employed, which is defined as^[24]Γ=∫LN|E(x,y)|2dxdy∫∞|E(x,y)|2dxdy.(1)

The mode profiles of different waveguide modes are calculated using the Lumerical MODE solution. The simulated results are shown in Figs. 4(b)–4(e). The confinement factors of the TE0 mode in the single-mode waveguide and the TE0, TE1, and TE2 modes in the multimode waveguide are calculated to be 96.4%, 98.9%, 98.9%, and 98.8%, respectively. Significantly improved confinement can be observed for the multimode waveguide, which would lead to the enhanced modulation efficiency as well as the reduced waveguide loss due to sidewall-roughness for each mode.

To characterize the high-speed performance of the present modulator, we first carried out the frequency response measurement of the device in terms of the EO S parameter. A 43-GHz vector network analyzer (VNA, Anritsu, MS46322B) was utilized, and the measured EO-S₂₁ curve was normalized to 100 MHz. The measured result is shown in Fig. 5. The measured 3-dB bandwidth of the device is 12 GHz. It should be noted that the peak around 8 GHz in the EO curve results from the interference signal in the environment and is not caused by the proposed device. For a lumped electrode-driven modulator, the EO frequency response of the device is subjected to two limitations. The first is the resistance-capacitance (RC)-limited bandwidth of the lumped electrode, and the second is the transit time of light through the device^[25]. The RC-limited bandwidth of the lumped electrode and the transit-time-limited bandwidth of the optical structure are theoretically estimated to be 52.9 GHz and 11.7 GHz, respectively. Therefore, the measured EO bandwidth of the device is mainly limited by the transit time of light through the device.

To verify the high-speed modulation performance of the device, we further set up the data transmission experiment. The experimental setup is shown in Fig. 6(a). A 27−1 non-return-to-zero (NRZ) pseudo-random binary sequence (PRBS) signal was generated from a 64-GSa/s arbitrary wave generator (AWG, Keysight, M8192A) and amplified by a radio frequency (RF) amplifier (SHFS807C). The signal was then applied to the modulator via a 40-GHz RF probe (GGB, Model 40 A). A tunable laser source of 10 dBm output power was used as the light input. The polarization was tuned to the TE mode with a polarization controller (PC). The output modulated light was amplified by an erbium-doped fiber amplifier (EDFA) to compensate for the on-chip optical loss and was received by a high-speed photodetector (PD) after passing through an optical bandpass filter (BPF). The photocurrent signal was finally sent to a digital communication analyzer (DCA) for eye diagram sampling.

The high-speed signal generated from the AWG has a Vpp of 1 V. After being amplified by the RF amplifier, the Vpp of the drive swing on the modulator is 4.8 V. The measured eye diagrams of the 10, 15, and 20 Gb/s on-off keying (OOK) signals are shown in Figs. 6(b), 6(c), and 6(d), respectively. The OOK signals with higher data rates were limited by the high half-wave voltage of the device and the limited gain of the RF amplifier. The limited ER is mainly due to the 0.5-mm length of the phase shifter as well as the imbalance of the two arms of the MZ structure. In our design, each arm is composed of four mode converters and a multimode waveguide. Any structural deviation caused by a fabrication error will degrade the balance between the upper and lower arms. Moreover, the metal electrode pattern will have a certain offset from the waveguide layer, which will cause the waveguide center to deviate from the middle of the ground and signal electrodes, thus creating different absorption losses caused by the electrode to the upper and lower arms. In order to increase the extinction ratio (ER) of the modulator, UV lithography with higher alignment accuracy needs to be adopted to balance the absorption loss brought by the electrode pattern misalignment.

Table 1 summarizes the performances of the TFLN interferometric modulator with high modulation efficiency. Thanks to the proposed mode-folded phase shifter structure, our device features a high modulation efficiency with a low VπL of 1 V·cm. The high modulation efficiency is mainly attributed to the multiple interactions of the optical signal within the mode-folded phase shifter and the enhanced optical confinement facilitated by the multimode waveguide. The modulation bandwidth of the proposed modulator is primarily delimited by the prolonged transit time within the loop-back waveguide structure, wherein mode conversion occurs. To address this constraint, an optimized mode converter featuring a shorter length could be employed to increase the modulation bandwidth of the device.

The modulation efficiency of the proposed device can be further optimized by minimizing the separation between the signal and ground electrodes. In our design, due to an alignment deviation of 4 µm in UV lithography, the distance between the electrode edge and the waveguide edge is set to 5 µm to ensure that there is no overlap between the electrode patterns and the waveguide patterns. With a reported separation of 1.5 µm between the electrode edge and the waveguide edge^[7], an 8.66 µm electrode gap can be expected with the same multimode waveguide width and thus the VπL of the proposed modulator could be further improved to 0.56 V·cm.

In summary, we have introduced and experimentally demonstrated an innovative TFLN MZM characterized by a high modulation efficiency achieved through the adoption of a mode-folded phase shifter. This accomplishment is attained without any compromise on the operational wavelength range of the device. High modulation efficiency with a low VπL of 1 V·cm has been attained. The modulator exhibits an electro-optic modulation bandwidth of 12 GHz. Experimental results validate the feasibility of 20 Gb/s OOK signaling using the proposed modulator. The high modulation efficiency is attributed to the carefully designed multimode phase shifter structure. The proposed mode-folded phase shifter slows down the light while sidestepping mutual interference, thereby enabling the device to have the capacity to support a wide operating wavelength range. We believe that this work offers a novel perspective on the realization of TFLN modulators characterized by a compact footprint and exceptional modulation capabilities.