††thanks: These authors contributed equally to this work.††thanks: These
authors contributed equally to this work.††thanks: These authors contributed
equally to this work.

# A heterogeneously integrated lithium niobate-on-silicon nitride photonic
platform

Mikhail Churaev  Institute of Physics, Swiss Federal Institute of Technology
Lausanne (EPFL), CH-1015 Lausanne, Switzerland  Rui Ning Wang  Institute of
Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015
Lausanne, Switzerland  Viacheslav Snigirev  Institute of Physics, Swiss
Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
Annina Riedhauser  IBM Research - Europe, Zurich, Säumerstrasse 4, CH-8803
Rüschlikon, Switzerland  Terence Blésin  Institute of Physics, Swiss Federal
Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
Charles Möhl  IBM Research - Europe, Zurich, Säumerstrasse 4, CH-8803
Rüschlikon, Switzerland  Miles A. Anderson  Institute of Physics, Swiss
Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
Anat Siddharth  Institute of Physics, Swiss Federal Institute of Technology
Lausanne (EPFL), CH-1015 Lausanne, Switzerland  Youri Popoff  IBM Research -
Europe, Zurich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland  Integrated
Systems Laboratory, Swiss Federal Institute of Technology Zurich (ETH Zürich),
CH-8092 Zürich, Switzerland  Ute Drechsler  IBM Research - Europe, Zurich,
Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland  Daniele Caimi  IBM Research
- Europe, Zurich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland  Simon Hönl
IBM Research - Europe, Zurich, Säumerstrasse 4, CH-8803 Rüschlikon,
Switzerland  Johann Riemensberger  Institute of Physics, Swiss Federal
Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland  Junqiu
Liu  Institute of Physics, Swiss Federal Institute of Technology Lausanne
(EPFL), CH-1015 Lausanne, Switzerland  Paul Seidler<EMAIL_ADDRESS>IBM
Research - Europe, Zurich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland
Tobias J. Kippenberg<EMAIL_ADDRESS>Institute of Physics, Swiss
Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland

The availability of thin-film lithium niobate on insulator (LNOI) and advances
in processing have led to the emergence of fully integrated LiNbO3 electro-
optic devices[1, 2, 3, 4], including low-voltage[5], high-speed modulators[6],
electro-optic frequency combs[7], and microwave-optical transducers [8, 9].
Yet to date, LiNbO3 photonic integrated circuits (PICs) have mostly been
fabricated using non-standard etching techniques that lack the reproducibility
routinely achieved in silicon photonics. Widespread future application of
thin-film LiNbO3 requires a reliable and scalable solution using standard
processing and precise lithographic control. Here we demonstrate a
heterogeneously integrated LiNbO3 photonic platform that overcomes the
abovementioned challenges by employing wafer-scale bonding of thin-film LiNbO3
to planarized low-loss silicon nitride (Si3N4) photonic integrated
circuits[10], a mature foundry-grade integrated photonic platform. The
resulting devices combine the substantial Pockels effect of LiNbO3 with the
scalability, high-yield, and complexity of the underlying Si3N4 PICs.
Importantly, the platform maintains the low propagation loss ($\mathbf{<0.1}$
dB/cm) and efficient fiber-to-chip coupling ($<$2.5 dB per facet) of the Si3N4
waveguides. We find that ten transitions between a mode confined in the Si3N4
PIC and the hybrid LiNbO3 mode produce less than 0.8 dB additional loss,
corresponding to a loss per transition not exceeding 0.1 dB. These nearly
lossless adiabatic transitions thus link the low-loss passive Si3N4 photonic
structures with electro-optic components. We demonstrate high-Q
microresonators, optical splitters, electrically tunable photonic dimers,
electro-optic frequency combs, and carrier-envelope phase detection of a
femtosecond laser on the same platform, thus providing a reliable and foundry-
ready solution to low-loss and complex LiNbO3 integrated photonic circuits.

Figure 1:  Hybrid integrated Lithium Niobate photonics.(a) Conventional
approaches to lithium niobate photonics, consisting of traditional Ti or
proton exchange based waveguides, and the recently emerged integrated
photonics based on etching of thin-film LNOI (which is mostly based on ridge
waveguides) (b) The hybrid approach presented in this work, based on
heterogeneous integration of thin film lithium niobate with Si3N4. (c)
Schematics of our approach which is based on wafer bonding of 4” (100 mm) thin
film lithium niobate onto planarized ultra low loss $\mathrm{Si_{3}N_{4}}$
photonic integrated circuits. (d) Hybrid optical mode profile for a typical
waveguide used in this work (cf Methods). (e) AFM measurements of the Si3N4
wafer before bonding showing 400 pm RMS roughness over 5 $\mu$m by 5 $\mu$m
field of view. (f) Long-range profilometry scan of the wafer before bonding.
(g) False-coloured scanning electron micrograph showing the hybrid structure.

Modern society has an constantly increasing demand for optical communications
bandwidth, with aggregate data rates doubling every 18 months[11, 12], and
optical technology is coming ever closer to the central processing units[13].
Optical modulators play a crucial role in this context, providing the means to
transfer electronic signals to optical carriers. With the rise of commercial
integrated photonics [14], a wide variety of modulation platforms have been
demonstrated that are compatible with wafer-scale manufacturing, among which
silicon and indium phosphide are the most prominent [15, 16, 17, 18]. In the
last decade, alternative systems, including organic hybrids [19, 20],
plasmonic devices [21], and modulators based on two-dimensional materials [22,
23, 24, 25] have also been developed. Among all the materials used, lithium
niobate (LiNbO3) remains the most preferable because of its excellent physical
properties, and commercial availability [26]. Advances in wafer-scale transfer
of LiNbO3 thin-films via the SmartCut${}^{\textbf{TM}}$ technique, combined
with improvements in etching of LiNbO3, have enabled low-loss integrated
electro-optics [27, 28, 29]. This has led to several key demonstrations,
including ultra-high-$Q$ optical microresonators[28], efficient electro-optic
frequency comb generation[7], frequency converters [30], and non-reciprocal
devices [31, 32]. In addition, electro-optic modulation both at CMOS voltage
levels and at high speed (up to 100 GHz) has been achieved [5, 6], offering
routes toward compact integrated LiNbO3 modulators compatible with CMOS
microelectronics for applications ranging from classical communication for 5G
cellular networks and datacenter interconnects to quantum interfaces for
microwave-optical conversion [33, 34, 35], and topological photonics employing
synthetic dimensions [36, 37]. Besides the electro-optic applications,
integrated LiNbO3 PICs are also of high interest for nonlinear photonics, for
example, for efficient second-harmonic generation, optical squeezing, and
parametric amplification [38, 39, 40].

Despite the achievements to date, widespread adoption of LiNbO3 integrated
photonics is still impeded by several key issues. Current LNOI-based devices
are fabricated using specific non-conventional ion-beam etching (IBE) to
achieve smooth waveguide surfaces. Insufficient etch-mask selectivity leads to
the formation of shallow ridge waveguides that require more challenging
process control to achieve the desired geometries. This complicates the
establishment of a reliable process design kit (PDK) for integrated LiNbO3
platforms. Second, edge coupling between fibers and chips is challenging, as
the ridge waveguide structures demonstrated so far show significant coupling
loss, 5 to 10 dB per facet, [30] unless more complicated double-etching
techniques are used [41, 42]. Third, while record resonance quality factors (Q
$\approx$ 107, linear loss of 0.027 dB/cm) have been reported in LiNbO3
microresonators[28], this has only been demonstrated for selected optical
resonances and has not been achieved broadly in other recently reported works,
where losses are typically one order of magnitude higher (0.2 - 0.3 dB/cm, see
Supplementary Table 1 for comparison). For future applications, uniformly low
loss across a wafer using precise and mature lithographic processes, along
with efficient coupling, are necessary to develop a foundry-level technology
that includes PDKs with, e.g., splitters, arrayed-waveguide gratings, optical
filters or beamforming networks.

As an alternative to conventional bulk LiNbO3 and ridge-waveguide-based
photonic devices, hybrid platforms combining thin-film LiNbO3 with waveguides
made of Si, Si3N4, or Ta2O5 have been recently developed[43, 44, 45] (see Fig
1(a)-(c)). With proper geometry optimization, the heterogeneously integrated
LNOI devices can reach electro-optic performance comparable to that of the
all-LNOI platforms[46] ($\mathrm{V_{\pi}L}=2.3$ V$\cdot$cm). Heterogeneous
integration using the organic adhesive benzocyclobutene (BCB) to bond LNOI to
silicon and direct bonding of chiplets to silicon and silicon nitride PICs has
been demonstrated, leading to modulators operating at CMOS voltages [47, 44].
Even though the low-loss operation of hybrid Si3N4-LiNbO3 waveguides was
reported [48, 49], the previous works did not provide reliable studies of
wafer-scale uniformity, dispersion, insertion loss, or other essential aspects
of photonic integrated circuits. The approaches were aimed at specific device
applications and could not demonstrate all the benefits of heterogeneous
integration of LiNbO3 with a well-developed photonic platform. Moreover, the
wafer-level bonding required to achieve scalable PDKs was not shown. Here, we
demonstrate a high-yield, low-loss, integrated LiNbO3-Si3N4 photonic platform
that solves multiple issues of LNOI integrated photonics. The approach
circumvents the need for optimized IBE etching of LiNbO3 and opens up the
possibility of creating a wide range of low-loss integrated electro-optic
photonic circuits. This is achieved by wafer-scale heterogeneous integration
[50, 48] (i.e. direct wafer bonding [51]) of an LNOI wafer onto a patterned
and planarized ultra-low-loss Si3N4 substrate as depicted in Fig 1(c). Our
approach combines the maturity of Si3N4 integrated photonics with the large
Pockels effect of LiNbO3 and enables complex, hybrid PICs that incorporate
passive Si3N4 and electro-optic LiNbO3 and exhibit ultra-low propagation loss
(8.5 dB/m).

Figure 2:  Optical loss measurements of the hybrid devices. (a) Photograph of
a fully bonded 2” lithium niobate wafer to a 4” photonic damascene wafer. (b)
Schematics of the chip facet with lithium niobate removed from the silicon
nitride inverse tapers. FDTD simulations of the mode transition at interface.
(c) Broadband transmission measurements of a 100 GHz FSR ring showing flat
coupling of resonances from 1260 nm to 1630 nm wavelength. (d) Extracted
integrated dispersion of the device. The inset shows a zoom-in of one of the
modes at 184 THz with amplitude modulation sidebands at 500 MHz and the
corresponding fitting curve. (e) Wafer map with averaged linewidth indicated
for the reference 21 GHz FSR rings. (f) Simulated optical mode confinement in
LiNbO3 as a function of optical frequency. Insets show typical mode profiles.
Grey-shadowed area represents the measurement bandwidth. (g) Loaded (red),
intrinsic (green), and coupling (blue) linewidth of the resonances presented
in (c). (h) Measured linewidth of 3 types of devices on the wafer accumulated
over 55 THz measurement bandwidth.

Fabrication process. The process flow for our hybrid PICs starts with the
fabrication of Si3N4 waveguide structures using the photonic Damascene process
[52, 10]. We use a 100 mm-diameter silicon wafer with 4 $\mu$m-thick wet
thermal SiO2, followed by deep-ultraviolet (DUV) stepper lithography, preform
dry etching, preform reflow, low-pressure chemical vapor deposition (LPCVD)
deposition of Si3N4, chemical-mechanical polishing (CMP), and SiO2 interlayer
deposition and annealing, as detailed in the Supplementary Information. The
Si3N4 photonic Damascene process is free of crack formation in the highly
tensile LPCVD Si3N4 film and provides high fabrication yield and ultra-low
propagation loss (1 dB/m). In addition, double-inverse nanotapers [53] are
incorporated for efficient edge coupling to lensed fibers. Previous devices
fabricated using this process have been the workhorse for numerous system-
level applications of soliton microcombs, ranging from coherent
telecommunication [54] to astrophysical spectrometer calibration [55] to
supercontinuum generation [56] and turnkey soliton generation [57].

One of the key advantages of the photonic Damascene process is the possibility
of obtaining an extremely flat wafer surface suitable for heterogeneous
integration. Specifically, we perform CMP on the SiO2 interlayer and bond the
fabricated Si3N4 Damascene substrate to a commercially available LNOI wafer
(NanoLN). The most critical constraints for achieving high bonding yield, the
surface roughness and topography, are measured prior to bonding. With CMP, the
long-range topography is reduced to a few nanometers over several hundred
microns, as shown in Fig. 1(f). Moreover, atomic force microscopy (AFM)
measurements over a range of a few microns reveal a root-mean-square (RMS)
roughness of 400 pm (Fig. 1(e)). This roughness level is sufficiently low for
direct wafer bonding. The donor and the acceptor wafer (the Si3N4 substrate
and the LNOI wafer, respectively) are cleaned, and both are coated by atomic
layer deposition (ALD) with a few nanometers of alumina (Al2O3). The wafers
are then bonded and annealed at 250∘C to enhance the bonding strength. See SI
for more technical information on fabrication. We have successfully bonded
several wafers, including whole 100-mm LNOI wafers, with a bonding yield close
to 100%, as evidenced by photoacoustic spectroscopy. Subsequent back-end
processing and electrode integration are described in the SI. A scanning
electron microscope image (Fig. 1(g)) of a cross-section of the layer
structure reveals clean bonding results. Finite-element-method simulations
(see Fig. 1(d)) indicate that, for the waveguide and wafer parameters used
here (cf. SI for waveguide geometry), the optical mode confinement factor for
LiNbO3 at the telecommunication wavelength of 1550 nm is
$\Gamma=\iint_{\mathrm{LiNbO_{3}}}|E|^{2}dS/\iint_{\mathrm{\Omega}}|E|^{2}dS=12\%$,
where $\Omega$ denotes the whole cross-section area. To demonstrate the
electro-optic capabilities of the heterogeneously integrated LiNbO3 photonic
circuits, we deposit tungsten ($\mathrm{W}$) electrodes on top of the LiNbO3
adjacent to the waveguides with an electrode-electrode gap of 6 $\mu$m.

To illustrate the versatility, lithographic precision, complexity, and yield
of the hybrid platform, we design a reticle with various devices. Figure 2(e)
shows the design layout of the Si3N4 photonic circuits for a 100-mm wafer; it
contains nine fields with 16 chips each – in total, more than 100 chips with
dimensions of 5 mm $\times$ 5 mm. The reticle includes chips with three
different types of devices: (1) microresonators with a free spectral range
(FSR) of either 100 GHz or 21 GHz, the former being used for electro-optic
comb generation; (2) photonic molecules consisting of a pair of coupled
microresonators each with a FSR of 50 GHz, as used for microwave-optical
conversion schemes; and (3) waveguides with a length of several centimeters
for supercontinuum generation (wafer D67b01).

Figure 3: Adiabatic mode transitions and hybrid optical splitters. (a) Colored
SEM image of a LiNbO3 taper fabricated to make a smooth optical mode
transition. (b) Optical microscope image of a chip used to estimate the
performance of interface tapers. Horizontal dotted lines mark waveguides with
two interface transitions (blue), four interface transitions (red), and six
interface transitions (green). The inset shows a zoom-in of a breakout region.
(c) Schematic of a tapered (adiabatic) interface transition. (d) Transmission
measurements of breakout waveguides described in (b) as well as a typical
straight (non-adiabatic) transition for comparison (orange line). (e)
Schematic of a straight (non-adiabatic) interface transition. (f) Transmission
measurements of waveguides with straight transition breakouts. (g) Optical
image, FDTD simulation, and schematic of a W-type 3-dB splitter. The geometry
is defined by the underlying Si3N4 layer. (h) Transmission measurements of two
ports of the splitter together with the transmission of a straight waveguide
as reference.

Optical loss characterization. Linear propagation loss is crucial in
determining the performance of integrated electro-optic devices, as it limits
the length of electro-optic modulators and the complexity of the associated
photonic circuit. To measure the linear optical loss, evanescent coupling
properties, and group velocity dispersion (GVD) of the hybrid structures, we
perform broadband frequency-comb-assisted spectroscopy [58] of multiple
microresonators across the entire wafer with three different external-cavity
diode lasers covering the wavelength ranges of 1260–1360 nm, 1355–1505 nm, and
1500–1630 nm. The intrinsic quality factors of individual 100 GHz microring
resonators reach up to $Q=3\times 10^{6}$, while the 50 GHz photonic dimers
(i.e., coupled microrings) and 21 GHz single rings exhibit even higher quality
factors up to $Q=4.5\times 10^{6}$. The latter corresponds to a linear
propagation loss of 8.5 dB/m. We observe an absorption peak at approximately
1420 nm (207 THz), which we associate with an overtone of OH-bond vibrations
in lithium niobate [59, 60]. As shown in Fig 2(g), optical losses rise with
increasing optical frequency. We associate this dependency with increased
whispering-gallery (radiation) loss as the mode shifts into the LiNbO3 thin
film at higher frequencies and becomes less confined (see Fig 2(f)). For the
same reason, we observe nearly uniform evanescent coupling of optical
microresonators over a span of 55 THz. The layout in Fig 2(e) is labeled with
the most probable linewidth measured for 21 GHz microresonators in various
regions, indicating the degree of variation across the wafer (see
Supplementary Information). These results not only demonstrate high yield and
wafer-scale fabrication but include some of the highest quality factors
achieved to date with integrated LiNbO3 devices. Notably, the $Q$s reported
here are not isolated values as in prior work on ridge resonators[28] but are
consistently high, i.e., we measure hundreds of resonances with $Q$ above
$4\times 10^{6}$ (linewidth below 50 MHz), as shown in Fig. 2(h).

Our hybrid platform also offers the possibility of precise dispersion
engineering; due to the interplay between material dispersion and the optical
mode distribution, the dispersion can be adjusted by varying the Si3N4
waveguide geometry or the LiNbO3 thickness. In this work, we designed the
structure to work in the near-zero GVD regime advantageous for broadband
optical frequency comb generation. As shown in Fig. 2(d) for a microresonator
with a FSR of 100 GHz, the measured integrated microresonator dispersion
($D_{\text{int}}$) only varies by 15 GHz over an optical bandwidth of 55 THz.
Interestingly, there is no constraint preventing the design of devices that
are uniformly coupled over a broad frequency range and, at the same time, have
extremely small dispersion.

Figure 4:  Electro-optic frequency comb generation and tunable dimers using
heterogenously integrated $\mathrm{LiNbO_{3}}$ photonic circuits. (a)
Experimental setup for electro-optic frequency comb generation. MWG -
microwave generator, MWA - microwave amplifier, OSA - optical spectrum
analyser. (b) Mode coupling schematics and integrated dispersion of the
measured device.(c) Measured optical spectrum of the generated EO comb at 1552
nm central frequency. Dashed line corresponds to numerical simulations with
phase modulation amplitude $\beta$ = 0.14 $\pi$. (d) Examples of EO frequency
combs generated at 4 other pump wavelength. (e) Photonic dimer image and mode
hybridization illustration. (f) High-Q resonance splitting of a photonic dimer
without additional biasing. S - symmetric supermode, AS - antisymmetric. (g)
DC tuning of the photonic dimer mode hybridization, corresponding to linear
tuning of around 30 MHz/V for a single mode. (h) Echelle plot of the photonic
dimer transmission, showing mode hybridization over a broadband scanning
range.

Fiber-chip coupling and interface transitions. Efficient input coupling from
an optical fiber to the photonic chip is paramount for numerous applications.
For air-cladded LiNbO3 ridge waveguides, inverse tapers lead to fiber-chip
edge-coupling losses of around 10 dB per facet unless complicated multi-layer
etching is used[41, 61, 62]. This is due to the significant mode mismatch
between the lensed fiber mode (typically circular with about 2.5 $\mu$m
diameter) and the asymmetric mode of partially etched air-cladded ridge
waveguide structures. Some recent work on integrated LiNbO3 devices
demonstrated the possibility of using embedded silicon edge-couplers to
overcome this challenge[6]. In our case, the relative indices of refraction of
the materials would lead to significant coupling loss if the LiNbO3 layer
remained on top of underlying Si3N4 inverse tapers. Hence, we remove the
LiNbO3 from the coupling regions and rely on standard Damascene Si3N4 inverse
tapers[53]. While this provides an efficient input coupling, there remains the
challenge of the transition between the regions with and without LiNbO3. To
address this issue, we designed and implemented adiabatic tapers in the LiNbO3
layer, as shown in Fig.3(c). The tapers are 100 $\mathrm{\mu}$m long with a
tip width of 500 nm and a final width of 10 $\mathrm{\mu}$m. Both film removal
and etching of the tapers are done in a single fabrication step using argon
ion-beam etching with a photoresist etch mask (see the Supplementary
Information for details on taper fabrication). All the functional photonic
components do not depend on the etching of the chip interface, which is
employed only at mode transition regions and, due to the short taper length,
does not require low roughness. We thus keep the LiNbO3 layer unprocessed for
all the photonic components, where both roughness and precise alignment are
critical to achieving low optical losses.

To measure the efficiency of the adiabatic transitions and remove the
ambiguity associated with the fiber-chip coupling loss from the measurement,
we designed an experiment in which we introduce multiple breakouts on straight
waveguides, where the optical mode experiences transitions from Si3N4
waveguides into the hybridized mode and back as depicted in Fig. 3(b). We
fabricated waveguides with 2, 4, 6, and 10 transitions (input/output tapers
and 0, 1, 2, and 4 breakouts, respectively) to determine the increase in loss
due to each transition. Figure 3(d) shows the results of these measurements.
As a reference, we compare them with straight interfaces (schematic in
Fig.3(e)). As can be seen in Figure 3(f), each straight transition leads to
approximately 1 dB loss, whereas the tapered input/output behaves in this
measurement as a virtually lossless transition. Strikingly, for the case of
the tapered transitions, we observe hardly any difference between 2, 4 and 6
interfaces, as shown in Figure 3(d) and approximately only 0.8 dB additional
loss for ten interfaces. Considering the statistical uncertainty in the
measurements, we deduce a transition loss of $<$0.1 dB per taper. Calibration
of the transmission measurements is discussed in the Supplementary
Information.

The lithographic precision of the Si3N4 photonic circuit layer provides our
heterogeneous integration approach with versatiliy and robustness, as
confirmed by the implementation of a W-shaped 3-dB splitter/coupler[63] (see
Fig. 3(g)) that uses the hybrid Si3N4-LiNbO3 mode but is defined solely by
underlying Si3N4 inverse tapers. Splitters are important components for many
optical devices, such as electro-optic modulators, optical networks, and
lasers based on reflective semiconductor optical amplifiers. The elegance of
this type of splitter is in its simplicity of design. Due to the presence of
the LiNbO3 slab and the single-mode nature of our hybrid waveguides, the
optical mode is adiabatically transferred from the input arm to the output
arms. We make the tapered sections 100 $\mu$m long, ensuring a small footprint
for integrated components exploiting this design. Transmission measurements of
the device reveal a flat response, with power asymmetry between the two arms
not exceeding 1.7 dB and on-chip insertion loss not exceeding 1 dB in the
1500-1620 nm wavelength range (Fig.3(h)).

Electro-optic devices. To demonstrate the electro-optic performance achievable
with our high-quality factor, hybrid LiNbO3 microresonators, we generate
electro-optic frequency combs in the 21 GHz resonators pumped resonantly in
the telecommunications C-band. We apply a high-power microwave signal with a
frequency 20.97 GHz across the integrated electrodes such that microwave-
induced sidebands are resonantly enhanced (Fig 4(a)-(b)). Even though only 12%
of the optical mode is confined inside the lithium niobate, it is enough to
achieve strong modulation of the optical phase. We observe around 60 sidebands
within a 25 dB span for an injected RF power of 40 dBm, as depicted in Fig
4(c). In this experiment, the phase modulation amplitude corresponds to
approximately 0.14$\mathrm{\pi}$ (see Supplementary Information). The electro-
optic coupling is enhanced due to the device’s high quality factor and flat
dispersion. We also make use of the previously mentioned homogeneous coupling
of our hybrid devices at optical wavelengths ranging from 1260 nm to 1630 nm
to generate electro-optic comb at five different pump wavelengths (1290 nm,
1345 nm, 1500 nm, 1550 nm, and 1625 nm) on a single device (Fig 4(d)).
Moreover, according to the simulations, the geometry can be optimized for
maximum electro-optic efficiency with a characteristic $\mathrm{V_{\pi}\cdot
L}$ product comparable to (2x larger than) the performance of X-cut ridge-
waveguide platforms[5]. The reason is that, in ridge waveguides, most of the
electro-optic interaction occurs not in the ridge itself, but in the slab
layer, where the modulating electric field is a factor of magnitude stronger
(see Supplementary Information). Therefore, the ridge waveguides and hybrid
waveguides are conceptually similar in terms of electro-optic interactions
(i.e., the role of the slab in ridge waveguides is being taken over by the
bonded LiNbO3 layer in our hybrid structure). Similar studies on optimization
of electro-optic performance of heterogeneously integrated LiNbO3 devices can
also be found elsewhere[46]. As a further example of the electro-optic
capabilities, we fabricate photonic dimers, which are known building blocks
for quantum coherent transducers based on cavity electro-optics[64, 34, 65, 9,
66]. Figure 4(g) shows the mode hybridization in the system as a function of
the applied DC voltage. We observe frequency tuning of 30 MHz/V when a DC
voltage is applied to one of the rings. Moreover, the precise and mature
fabrication of the Si3N4 waveguides enables the creation of high-Q photonic
dimers exhibiting broadband normal mode splitting even at zero-bias (cf Figure
4(f)-(h)). The presence of avoided mode crossings for the symmetric supermode
(lower frequency) is common with the photonic dimer configuration[67]. In one
last experiment exploiting the $\chi^{(2)}$ nonlinearity of the LiNbO3, we
perform supercontinuum generation in the hybrid waveguides. We observe octave-
spanning supercontinuum generation mediated by the $\chi^{(3)}$ nonlinearity,
together with simultaneous second-harmonic generation due to the optical field
in the LiNbO3, allowing direct measurement of the carrier-envelope offset
frequency of the femtosecond pulse laser used as a pump. The details of this
experiment can be found in the Supplementary Information.

Summary. To conclude, we have demonstrated a hybrid Si3N4-LiNbO3 platform for
photonic integrated circuits using direct wafer-scale bonding that endows the
mature Si3N4 Damascene technology with the second-order nonlinearity
($\chi^{(2)}$ / Pockels effect) of LiNbO3. The heterogeneous integration
preserves the precise lithographic control, low propagation loss, and
efficient fiber-to-chip coupling of the underlying Si3N4 waveguides for use in
a variety of important photonic building blocks. We have also presented a
design for the transition from Si3N4 waveguides to hybrid Si3N4-LiNbO3
waveguides with a measured insertion loss not exceeding 0.1 dB per interface.
The ability to achieve low-loss transitions is essential for the realization
of complex devices, providing a bridge between passive silicon nitride
photonics and electro-optic devices. To the best of our knowledge, this is the
first time a heterogeneously integrated LiNbO3 photonic platform combines all
the beneficial features of Si3N4 PICs at wafer scale. A comparison of the
simultaneously achieved desirable features is given in Supplementary Table 1.
With further geometry optimization, the electro-optic performance can reach
levels comparable to that of ridge waveguide structures while keeping
propagation losses independent of the quality of the LiNbO3 etching. Possible
applications of our platform include photonic switching networks for
neuromorphic or quantum computing, devices for quantum state transduction from
microwave to optical photons, integrated electro-optic frequency comb sources,
on-chip generation of second-harmonic and squeezed light, as well as high-
speed electro-optic devices for optical communications or rapidly tunable,
low-noise lasers.

Acknowledgments: We thank the Operations Team of the Binnig and Rohrer
Nanotechnology Center (BRNC), and especially Diana Davila Pineda and Ronald
Grundbacher, for their help and support. Silicon nitride substrates were
fabricated in the EPFL center of MicroNanoTechnology (CMi). We also thank
Aleksandr Tusnin for his help in numerical simulations.

Funding Information: This work was supported by funding from the European
Union Horizon 2020 Research and Innovation Program under the Marie Skłodowska-
Curie grant agreement No. 722923 (OMT) and No. 812818 (MICROCOMB), as well as
under the FET-Proactive grant agreement No. 732894 (HOT). This work was also
supported by the Swiss National Science Foundation under grant agreement No.
176563 (BRIDGE) and 186364 (Sinergia).

Data Availability: The code and data used to produce the plots are available
from Zenodo.

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