Articles

https://doi.org/10.1038/s41566-019-0378-6

High-performance hybrid silicon and

lithium niobate Mach–Zehnder modulators
for 100 Gbit s−1 and beyond
Mingbo He1, Mengyue Xu1, Yuxuan Ren2, Jian Jian1, Ziliang Ruan2, Yongsheng Xu2, Shengqian Gao1,
Shihao Sun1, Xueqin Wen2, Lidan Zhou1, Lin Liu1, Changjian Guo2, Hui Chen1, Siyuan Yu1, Liu Liu 2* and
Xinlun Cai 1*

Optical modulators are at the heart of optical communication links. Ideally, they should feature low loss, low drive voltage, large
bandwidth, high linearity, compact footprint and low manufacturing cost. Unfortunately, these criteria have been achieved
only on separate occasions. Based on a silicon and lithium niobate hybrid integration platform, we demonstrate Mach–Zehnder
modulators that simultaneously fulfil these criteria. The presented device exhibits an insertion loss of 2.5 dB, voltage–length
product of 2.2 V cm in single-drive push–pull operation, high linearity, electro-optic bandwidth of at least 70 GHz and modula-
tion rates up to 112 Gbit s−1. The high-performance modulator is realized by seamless integration of a high-contrast waveguide
based on lithium niobate—a popular modulator material—with compact, low-loss silicon circuitry. The hybrid platform demon-
strated here allows for the combination of ‘best-in-breed’ active and passive components, opening up new avenues for future
high-speed, energy-efficient and cost-effective optical communication networks.

G
lobal data traffic has witnessed continuous growth over the devices with good confinement29–40, and LNOI modulators with a
past three decades due to the insatiable demands of modern low drive voltage and ultrahigh EO bandwidth have been recently
society1. This rapid expansion is placing a serious challenge demonstrated39,41,42.
on transceivers in all levels of optical networks—how to signifi- An alternative approach—hybrid integration of LN membranes
cantly increase data rates while reducing energy consumption and onto SOI PICs—has also attracted considerable interest43,44. The
cost2,3. To address this challenge, silicon photonics on the silicon- hybrid silicon/LN material system combines the scalability of sili-
on-insulator (SOI) platform has emerged as the leading technology con photonics with the excellent modulation performance of LN.
due to the possibility of low-cost and high-volume production of A few demonstrations of hybrid Si/LN optical modulators have
photonic integrated circuits (PICs) in CMOS foundries4–8. been reported, all of which rely on a supermode waveguide struc-
Optical modulators are key components serving as the infor- ture consisting of an unpatterned LN membrane on top of a sili-
mation encoding engines from the electrical domain to the optical con waveguide. This structure is designed to support a distributed
domain5. Optical modulation in silicon relies mainly on the free- optical mode that resides in both the LN and the underlying sili-
carrier dispersion effect9–14. Unfortunately, free-carrier dispersion is con waveguide (that is only part of the modal power overlaps with
intrinsically absorptive and nonlinear, which degrades the optical the LN region), which compromises the modulation efficiency. In
modulation amplitude (OMA) and may lead to signal distortion fact, the hybrid Si/LN optical modulators demonstrated so far show
when using advanced modulation formats. either low EO bandwidth or high operation voltage.
Tremendous efforts have been made towards realizing high- Here, we demonstrate hybrid Si/LN Mach–Zehnder modulators
performance optical modulators in various material platforms15–26. (MZMs) that employ two layers of hybrid integrated waveguides and
Among them, lithium niobate (LN) remains a preferred material vertical adiabatic couplers (VACs). The VACs transfer the optical
due to its excellent electro-optic (EO) modulation properties origi- power fully, rather than partially, between the silicon waveguide and
nating from the Pockels effect27,28. LN modulators show unrivaled LN membrane waveguide. This approach efficiently utilizes the LN
results for the generation of high-baud-rate multilevel signals and membrane and overcomes the trade-off in the previous approaches.
are still the best choice for ultra-long-haul links29. Conventional The proposed devices show a large EO bandwidth, high modulation
LN modulators are formed by low-index-contrast waveguides with efficiency, low on-chip insertion loss and high linearity. On–off keying
weak optical confinement, and the microwave electrodes must be (OOK) modulation up to 100 Gbit s−1 and four-level pulse amplitude
placed far away from the optical waveguide to minimize absorption modulation (PAM-4) up to 112 Gbit s−1 are successfully demonstrated.
losses, which leads to an increased drive voltage. As a result, con-
ventional LN modulators are bulky in size and low in modulation Results
efficiency (VπL > 10 V cm). Recently, LN membranes on insulator Design of hybrid silicon and LN MZMs. The devices were fab-
(LNOI) has emerged as a promising platform to form waveguide ricated based on benzocyclobuten (BCB) adhesive die-to-wafer

1
State Key Laboratory of Optoelectronic Materials and Technologies and School of Electronics and Information Technology, Sun Yat-sen University,
Guangzhou, China. 2Centre for Optical and Electromagnetic Research, Guangdong Provincial Key Laboratory of Optical Information Materials and
Technology, South China Academy of Advanced Optoelectronics, South China Normal University, Higher-Education Mega-Center, Guangzhou, China.
*e-mail: liu.liu@coer-scnu.org; caixlun5@mail.sysu.edu.cn

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Articles Nature Photonics
a b
t ws wg
h
w
Grating coupler
s Au
LN
LN waveguide
BCB
SiO2

Si

c d

G
S θ = 60°
G θ 2 μm

500 nm

e f
C
B
A
500 nm 500 nm 500 nm

500 nm 500 nm 500 nm

LN
BCB
Si waveguide
A B C

Fig. 1 | Structure of the hybrid Si/LN MZM. a, Schematic of the structure of the whole circuit. b, Schematic of the cross-section of the hybrid waveguide.
c, Scanning electron microscopy (SEM) image of the cross-section of the LN waveguide. d, SEM image of the metal electrodes and the optical waveguide.
e, Schematic of the VAC. f, SEM images of the cross-sections of the VAC at different positions (A, B, C) and calculated mode distributions associated with
the cross-sections. A rainbow style colour map is used to represent the mode-field intensities, where the red indicates the strongest intensity.

a 1.0
b 1.0

Vπ = 7.4 V
Transmission (a.u.)

0.8
0
Transmission(dB)

0.6 –10 Device L = 3 mm

–20
0.4 ER > 40 dB 0.75
–30
Normalized transmission

–40
0.2
–6 –4 –2 0 2 4 6
Voltage (V)
0
–6 –4 –2 0 2 4 6
0.5
Voltage (V)

1.0
Transmission spectra at quadrature
Transmission (a.u.)

0.8 Device L = 5 mm
0.25
0.6

0.4 Vπ = 5.1 V

0.2
0
0 1,530 1,535 1,540 1,545 1,550 1,555 1,560 1,565 1,570
–6 –4 –2 0 2 4 6
Wavelength (nm)
Voltage (V)

Fig. 2 | Static EO performance. a, Normalized optical transmission of the 3 mm and 5 mm devices as a function of the applied voltage, showing Vπ values of
7.4 V and 5.1 V, respectively. The inset shows the measured extinction ratio (ER) on a logarithmic scale. b, Measured spectral response of the MZM biased
at quadrature, indicating broadband operation of the device. a.u., arbitrary units.

bonding and LN dry-etching techniques. Figure 1a shows the where EO interactions (Pockels effect) occur. The bottom SOI cir-
schematic view of the present Si/LN hybrid MZM, consisting of cuit supports all other passive functions, consisting of two 3 dB
two waveguide layers and VACs. The top waveguides, formed by multimode interference (MMI) couplers that split and combine
dry-etching of an X-cut LN membrane, serve as phase modulators the optical power, and two grating couplers for off-chip coupling.

360 Nature Photonics | VOL 13 | MAY 2019 | 359–364 | www.nature.com/naturephotonics

Nature Photonics Articles
a c
VNA
RF RF RF spectrum
Combiner
PD source 2 source 1 analyser
Port1 Port2
Bias voltage Bias tee PD
Tunable laser
Tunable laser

PC PC
EDFA BPF EDFA BPF
Modulator chip Modulator chip

b d
0
Electro-optic S21 (dB)

3 Commercial, 1GHz
ntal
This work, 1GHz ame
0 Fund
This work, 10 GHz
–3
–3 dB –40
–6 D3

RF output power (dBm)

–9
Device L = 3 mm IM

–12
10 20 30 40 50 60 70
–80

95.2 dB
Frequency (GHz)
Hz

99.6 dB
G
Hz 10
Electro-optic S21 (dB)

94.9 dB
3 1G @
–120 @ or
0 or flo
flo ise
–3 ise No
–3 dB No
–6
Device L = 5 mm
–9 –160
–30 –20 –10 0 10 20 30 40
–12
10 20 30 40 50 60 70 RF input power (dBm)
Frequency (GHz)

Fig. 3 | EO bandwidth and linearity. a, Experimental set-up for measuring the EO bandwidth. VNA, vector network analyser; EDFA, erbium-doped fiber
amplifier; BPF, bandpass filter; PD, photodetector; PC, polarization controller. b, EO bandwidths (S21 parameter) of MZMs with lengths of 3 mm and 5 mm.
The 3 dB bandwidths of both devices are beyond the measurement limit of the VNA (70 GHz). c, Experimental set-up for measuring the IMD3 SFDR.
d, RF output power of the fundamental and IMD3 components as a function of RF input power for our device at 1 GHz and 10 GHz, and for a commercially
available LN MZM at 1 GHz. The noise floor is in 1 Hz bandwidth, limited by the RF spectral analyser.

The VACs, which were formed by silicon inverse tapers and super- ground and signal metals. To achieve a large EO bandwidth, the
imposed LN waveguides, serve as interfaces to couple light up and electrodes are operated in a travelling wave manner and opti-
down between the two layers. This hybrid integration architecture mized for impedance matching, as well as velocity matching of
offers two distinct advantages. First, since the task of routing light the microwave and light signals (Supplementary Section II). The
across the chip is placed on the underlying silicon waveguides, only thickness of electrodes was set to t = 600 nm, and the widths of
simple, straight waveguides need to be fabricated in the LN mem- signal and ground electrodes were designed as ws = 19.5 μm and
brane. This allows for a more compact device footprint and greater wg = 30 μm, respectively (Fig. 1b,d).
flexibility in the LN waveguide design, compared with that of devices The VAC is another important part of the device (Fig. 1e) and must
based on the pure LNOI platform. Second, the VACs, together with be optimized for high efficiency. The width of the silicon waveguide
the dry-etched LN waveguide design, facilitate high overlap between tapers from 500 nm to 80 nm over a length of 150 μm, whereas the
the optical modes and active material, as well as good optical con- width of the LN waveguide remains constant at 1 μm. The thickness
finement in LN waveguides. This enables more efficient utilization of the BCB is ~300 nm (that is, the gap between the bottom of the LN
of the LN active region, in contrast to other hybrid Si/LN hybrid waveguide and the top of the silicon waveguide is 80 nm), which is suf-
devices with unpatterned LN membranes. The schematic of the ficiently robust with respect to the variations induced by the fabrica-
cross-section of the hybrid waveguide is illustrated in Fig. 1b. tion processes. The measured coupling efficiency of the VAC is >97%
The LN waveguide is the most critical part of the present (loss of ~0.19 dB per VAC) (Supplementary Section III). It should be
device and has to be optimized to achieve high modulation effi- noted that simulation indicates that the silicon taper tip width can be
ciency and low optical loss. The fabricated waveguides have a top as large as 200 nm with negligible degradation in coupling efficiency,
width of w = 1 μm, a slab thickness of s = 420 nm, a rib height of which means the present design is compatible with standard mass
h = 180 nm and a sidewall angle of 60° (Fig. 1c). The lithography production processes (Supplementary Section III). Figure 1f presents
and etching processes were optimized to yield smooth sidewalls snapshots of the optical intensity patterns for various cross-sections of
and the LN waveguide features a measured propagation loss of the VAC, which illustrates the process of mode transfer.
0.98 dB cm−1 (Supplementary Section III). The gap between the
waveguides and electrodes was set to 2.75 μm. These parameters Static EO performance. Fabricated MZM devices with arm lengths
are designed to achieve a good balance between the modulation of 3 mm and 5 mm were measured in detail. The devices are driven
efficiency and optical losses (including both metal absorption in a single-drive push–pull configuration, so that applied voltage
and sidewall scattering loss) (Supplementary Section I). The elec- induces a positive phase shift in one arm and a negative phase shift
trodes are configured in a ground–signal–ground (GSG) form, in the other. Figure 2a shows the half-wave voltage measurements for
where the two LN waveguides lie in the two gaps between the both devices with a 100 kHz triangular voltage sweep; the half-wave

Nature Photonics | VOL 13 | MAY 2019 | 359–364 | www.nature.com/naturephotonics 361

Articles Nature Photonics

a
SHF
AWG
S807

Bias voltage Bias tee

Tunable laser

PC
EDFA BPF PD Oscilloscope
Modulator chip

b f

56 Gb s–1 OOK 56 Gb s–1 PAM-4 (28 Gbaud)

c g

72 Gb s–1 OOK 112 Gb s–1 PAM-4 (56 Gbaud)

d

h
10–2
FEC threshold 3.8×10–3

10–3
B2B BER

84 Gb s–1 OOK 56 Gb s–1 PAM4

e 10–4
112 Gb s–1 PAM4

10–5

10–6
–25 –20 –15 –10 –5
Received optical power (dBm)

100 Gb s–1 OOK

Fig. 4 | Data transmission testing. a, Experimental set-up for measuring the eye diagram. AWG, arbitrary waveform generator. b–e, Optical eye diagrams
for OOK signal at data rates of 56 Gb s−1 (b), 72 Gb s−1 (c), 84 Gb s−1 (d) and 100 Gb s−1 (e). The dynamic extinction ratios are 11.8 dB, 6.0 dB, 5.5 dB and
5.0 dB, respectively. f,g, Measured PAM-4 modulation optical eye diagrams at 28 Gbaud (50 Gb s−1) (f) and 56 Gbaud (112 Gb s−1) (g). h, Measured curves
of BER versus the received optical power for 28 Gbaud (56 Gb s−1) and 56 Gbaud (112 Gb s−1) PAM-4 signal.

voltages Vπ for the 3 mm and 5 mm devices are 7.4 V and 5.1 V, cor- device in the whole C-band. The Vπ value of the present device can be
responding to voltage–length products of 2.2 V cm and 2.5 V cm, further reduced by simply increasing the device length, as an LNOI
respectively. It should be noted that the voltage–length products are modulator with Vπ = 1.4 V was recently achieved with a device length
measured in a single-drive push–pull configuration and the value of 2 cm (ref. 39). For the proposed Si/LN hybrid modulator, Vπ of about
measured in a single arm will be increased by a factor of two. The 1 V is expected with a similar length. This would enable driverless
inset of Fig. 2a shows the optical transmission on a logarithmic scale, modulation from direct CMOS output without compromising the
indicating a measured extinction ratio of greater than 40 dB for the extinction ratio. In addition, a device with such a length can also fit
3 mm device. Figure 2b shows the measured spectral response of the in some common transceiver packages like QSFP (Quad Small Form-
MZM biased at quadrature, indicating broadband operation of the factor Pluggable) and can be adopted for future 400 G applications45.

362 Nature Photonics | VOL 13 | MAY 2019 | 359–364 | www.nature.com/naturephotonics

Nature Photonics Articles
Table 1 | Comparison of several performance metrics for hybrid silicon MZM
Loss Vπ EO bandwidth OOK data rate Length of modulation area
SOI 10
5.4 dB 7V 58 GHz 90 Gb s −1
2 mm
SOH20 11 dB 22 V >100 GHz NA 0.5 mm
SOH47 >11 dBa 0.9 V 25 GHz 100 Gb s−1 1.1 mm
SOH plasmonic48 12 dB >40 Vb >65 GHz 40 Gb s−1 29 μm
Si/BTO plasmonic 49
30 dB c
25 V >100 GHz 72 Gb s−1 10 μm
Si/BTO50 3.3 dBd 20 V 800 MHz 300 Mb s−1 0.75 mm
This work 2.5 dB 5.1 V >70 GHz 100 Gb s−1 5 mm
a
The value is calculated from 20 dB fibre-to-fibre loss and 9 dB off-chip coupling loss. The value is calculated from the reported VπL of 1.3 V mm and length of 29 μm. cThe value is calculated from
b

propagation loss of 2 dB µm−1 with 10 µm length, and 10 dB loss for two photonic-plasmonic converters. dThe value is calculated from propagation loss of 44 dB cm−1 with 0.75 mm length. NA, not available.

EO bandwidth and linearity. We then characterized the small-sig- It should be noted that approaches of combining silicon with
nal EO bandwidth (S21 parameter) of the fabricated devices using other materials exhibiting Pockels effects, such as organic materi-
the set-up shown in Fig. 3a. The measured 3 dB EO bandwidths of als and barium titanate (BTO), have also been reported. In Table 1,
both devices are greater than 70 GHz (Fig. 3b), which is beyond the we compare the performance of the present device with the state-
measurement limits of our vector network analyser (VNA). The of-the-art, including silicon–organic-hybrid (SOH) MZMs, SOH
measured EO bandwidth is much higher than that of pure silicon- plasmonic MZMs and BTO/Si plasmonic MZMs. Here, we focus on
based modulators. We believe that the EO bandwidth of the present MZMs with either large EO bandwidth or high operation speed, and
device could be extended beyond 100 GHz by further optimizing results of pure silicon modulators operating in the carrier depletion
the travelling-wave electrode (Supplementary Section II). mode are also included as a benchmark. As shown in Table 1, the
To characterize the linearity of the present device, we further present device in this work is the only one in which low Vπ and low
examine the third-order intermodulation (IMD3) spurious free insertion loss are achieved simultaneously. In particular, the inser-
dynamic range (SFDR) performance of the 3 mm device using the tion loss of the present device is much lower than that of all others,
set-up shown in Fig. 3c. To provide a comparative study, we also and to the best of our knowledge, this is the lowest insertion loss
measured the IMD3 SFDR of a commercially available LN MZM ever achieved in optical modulators operating above 40 Gbit s−1 on
(Fujitsu FTM7937EZ) with the same measurement system. Both silicon. The demonstrated Vπ of the present device is also promising,
devices are biased at quadrature and the optical power reaching which is only surpassed by the SOH modulator with a much higher
the photodetector after pre-amplification is kept at 0 dBm. For our insertion loss. As discussed above, Vπ can be further engineered to
device, the measured IMD3 SFDR is 99.6 dB Hz2/3 at 1 GHz (Fig. be about 1 V while maintaining an insertion loss of less than 4 dB.
3d), which is slightly better than that achieved by the commercial A low Vπ is critical for a travelling-wave type of modulator, since
LN MZM (94.9 dB Hz2/3). At 10 GHz, the measured SFDR decreases the energy consumption per bit is proportional to the square of the
slightly to 95.2 dB Hz2/3, mainly due to a higher noise floor of the driving voltage. For the data transmission experiments in Fig.4, the
measurement system. The SFDR value can be increased further by energy consumption of the present device of 3 mm length is esti-
increasing the received optical power. mated to be about 170 fJ per bit (see Supplementary Section II). It
has been recently proved that tens of aJ per bit energy consumption
Data transmission testing. Next, we evaluated the performance can be achieved for LN thin film modulators, although at a compro-
of the 3 mm device for high-speed digital data transmission, as mised BER39. We believe that a similar performance can be expected
depicted in Fig. 4a. First, the OOK modulations were applied to the for the present Si/LN hybrid device, since the cross-section struc-
device. Figure 4b–e summarizes the optical eye diagrams at 56, 72, tures of the phase shifter section are very similar for the two cases.
84 and 100 Gb s−1. The measured extinction ratios are 11.8, 6.0, 5.5 Another approach for decreasing the energy consumption is to use a
and 5.0 dB, respectively. It is noteworthy that at 100 Gb s−1 the whole resonant device with lumped electrodes instead of a travelling-wave
measurement system is already limited by the bandwidth of the design32,35, but the working wavelength band, in this case, is limited.
radiofrequency (RF) probe and cables. PAM-4 modulation experi- The underlying silicon waveguides not only route light with
ments were also carried out with the same experimental set-up. The low losses across the chip, but also allow integration of the present
optical PAM-4 eye-diagrams at 28 Gbaud and 56 Gbaud are shown modulator with the complete suite of silicon photonic components.
in Fig. 4f,g. The back to back (B2B) bit-error rate (BER) curves at This makes the proposed Si/LN platform highly desirable for new
both PAM-4 data rates, shown in Fig. 4h, decrease linearly as the emerging applications. For instance, future integrated microwave
received optical power before pre-amplification increases. No error photonic (MWP) systems would require on-chip linear modulators
floor is observed in the measured power range, and the error rates featuring high-fidelity electronic-to-optical conversion. The present
are also well below the hard-FEC limit of 3.8 × 10−3. device is ideal for this scenario and can be envisaged to be co-inte-
grated with passive SOI structures, such as Bragg gratings or micro-
Discussion resonators, to form sophisticated integrated MWP circuits. Another
As presented above, the hybrid Si/LN MZMs demonstrated here can possible application area could be linear optical quantum computing
achieve excellent optical modulation characteristics, while main- (LOQC)46. LOQC relies on universal quantum gates, which could
taining the key advantages of SOI photonic circuits. LN active wave- be implemented by adding auxiliary photons and by using rapid,
guides can be bonded and fabricated with lithographic precision time-of-flight feedforward. In practice, a feedforward step requires
and alignment accuracy in a back-end process after the SOI fabri- large-scale, low-loss, rapidly reconfigurable (in the gigahertz
cation. This manufacturing procedure is highly scalable and fully range) optical circuits capable of low-noise pure phase modula-
CMOS-compatible. Therefore, our approach potentially provides a tion—requirements that are attainable on our platform. The pres-
new generation of compact, high-performance optical modulators ent platform is also amenable to further integration with lasers and
for telecommunications and data-interconnects. detectors, as well as high-speed electronic drivers based on CMOS

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Articles Nature Photonics

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Author contributions
X.C. developed the idea. X.C. and L.L. conceived device design. M.H. and J.J. carried out
21. Lee, M. et al. Broadband modulation of light by using an electro-optic
the LN fabrication. M.H., S.G., H.C., L.Z., L.L. and S.S. carried out the silicon fabrication.
polymer. Science 298, 1401–1403 (2002).
M.H. and Y.R. carried out the bonding process. M.X., Z.R., Y.X., X.W. and C.G., carried
22. Han, J.-H. et al. Efficient low-loss InGaAsP/Si hybrid MOS optical modulator.
out the measurement. L.L. and X.C. carried out the data analysis. All authors contributed
Nat. Photon. 11, 486–490 (2017).
to the writing. X.C. finalized the paper. S.Y., L.L. and X.C. supervised the project.
23. Kikuchi, N., Yamada, E., Shibata, Y. & Ishii, H. High-speed InP-based
Mach–Zehnder modulator for advanced modulation formats. In Compound
Semiconductor Integrated Circuit Symposium (CSICS) 1–4 (IEEE, 2012). Competing interests
24. Phare, C. T., Lee, Y. H. D., Cardenas, J. & Lipson, M. Graphene electro-optic The authors declare no competing interests.
modulator with 30 GHz bandwidth. Nat. Photon. 9, 511–514 (2015).
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64–67 (2011). Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/
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(CRC Press, 2011). Correspondence and requests for materials should be addressed to L.L. or X.C.
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364 Nature Photonics | VOL 13 | MAY 2019 | 359–364 | www.nature.com/naturephotonics

Nature Photonics Articles
Methods bandwidth measurement, and the frequency response of the PD (XPDV4120R)
Fabrication. A standard SOI processing including e-beam lithography (EBL) is deduced from the measured S21 response. For linearity measurement, the input
and dry-etching processes was used to fabricate the grating coupler, 3 dB MMIs electrical signal consists of a DC bias and two RF tones with frequencies separated
and silicon inverse tapers. An LNOI sample with silicon substrate was flip- by 10 MHz and centred at the desired frequency. An RF spectrum analyser is
bonded to the SOI wafer using the BCB adhesive bonding process. The substrate used to analyse frequency components of the received electrical signal. For data
of the LNOI was removed by mechanical grinding and dry etching. Afterwards, transmission measurement, an arbitrary waveform generator (AWG, Micram)
hydrogen silsesquioxane (HSQ, FOX-16 by Dow Corning) was spin-coated on with a sampling rate of 100 gigasample per second is used to generate the electrical
the LN thin film for EBL. The waveguide patterns were transferred into LN with signals. A 50 GHz broadband amplifier (SHF 807) with an output saturation Vpp
optimized argon plasma etching in an inductively coupled plasma (ICP) etching of 4 V is used to amplify the driving signal to the modulator together with a DC
system. The physical etching by an argon plasma results in a sidewall angle bias. For OOK eye diagram measurements, the bias voltage is 0.7 V lower than the
of ~60°. Finally, the travelling wave electrodes were patterned through quadrature point to achieve better extinction ratios and the resultant additional
a liftoff process. loss is less than 0.5 dB. For PAM-4 eye diagram measurements, the modulator is
biased at the quadrature point and the levels of the driving signals are deduced
Dynamic measurement. The set-up for EO bandwidth, linearity and data from an inverse trigonometric function to compensate the typical sinusoidal
transmission measurements are shown in Figs. 3 and 4, respectively. The response of the Mach–Zehnder interferometer. Digital low-pass filters are also
electrical signal is fed to the device electrode through a 67-GHz-bandwidth RF applied to limit the signal bandwidth. For the bit-error rate measurements, the
probe (GGB 67A). A second RF probe (not shown) is also attached to the end detected signal is sampled by a real-time oscilloscope (Tektronics DPO73304) and
of the travelling-wave electrode, and a 50 Ω termination is applied to the second analysed using an off-line DSP, including resampling, equalization and symbol
probe for impedance matching. For the optical signal, light from a tunable laser decision (see Supplementary Section IV).
is coupled into and collected from the SOI grating couplers using single-mode
fibres. A polarization controller is used to ensure TE input polarization. The Data availability
received optical signal is pre-amplified and filtered through an erbium-doped fibre The data that support the plots within this paper and other findings of this study
amplifier (EDFA) and a bandpass filter (BPF) before detection. A VNA is used for are available from the corresponding author upon reasonable request.

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