††thanks: These authors contributed equally to this work.††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 chip-integrated comb-based microwave oscillator

Wei Sun  International Quantum Academy, Shenzhen 518048, China  Zhiyang Chen
International Quantum Academy, Shenzhen 518048, China  Shenzhen Institute for
Quantum Science and Engineering, Southern University of Science and
Technology, Shenzhen 518055, China  Linze Li  School of Information Science
and Technology, ShanghaiTech University, Shanghai 201210, China  Chen Shen
International Quantum Academy, Shenzhen 518048, China  Qaleido Photonics,
Hangzhou 310000, China  Jinbao Long  International Quantum Academy, Shenzhen
518048, China  Huamin Zheng  International Quantum Academy, Shenzhen 518048,
China  College of Electronics and Information Engineering, Shenzhen
University, Shenzhen 518000, China  Luyu Wang  School of Information Science
and Technology, ShanghaiTech University, Shanghai 201210, China  Qiushi Chen
School of Information Science and Technology, ShanghaiTech University,
Shanghai 201210, China  Zhouze Zhang  School of Information Science and
Technology, ShanghaiTech University, Shanghai 201210, China  Baoqi Shi
International Quantum Academy, Shenzhen 518048, China  Department of Optics
and Optical Engineering, University of Science and Technology of China, Hefei
230026, China  Shichang Li  International Quantum Academy, Shenzhen 518048,
China  Shenzhen Institute for Quantum Science and Engineering, Southern
University of Science and Technology, Shenzhen 518055, China  Lan Gao
International Quantum Academy, Shenzhen 518048, China  Shenzhen Institute for
Quantum Science and Engineering, Southern University of Science and
Technology, Shenzhen 518055, China  Yi-Han Luo  International Quantum Academy,
Shenzhen 518048, China  Baile Chen<EMAIL_ADDRESS>School of
Information Science and Technology, ShanghaiTech University, Shanghai 201210,
China  Junqiu Liu<EMAIL_ADDRESS>International Quantum Academy, Shenzhen
518048, China  Hefei National Laboratory, University of Science and Technology
of China, Hefei 230088, China

Low-noise microwave oscillators are cornerstones for wireless communication,
radar and clocks. The employment and optimization of optical frequency combs
have enabled photonic microwave synthesizers with unrivalled noise performance
and bandwidth breaking the bottleneck of those electronic counterparts Fortier
_et al._ (2011); Xie  _et al._ (2016); Li  _et al._ (2014); Nakamura  _et al._
(2020). Emerging interest has been concentrated on photonic microwave
generation using chip-based Kerr frequency combs, namely microcombs Kippenberg
_et al._ (2018); Pasquazi  _et al._ (2018). Today microcombs built on photonic
integrated circuits feature small size, weight and power consumption Moss  _et
al._ (2013); Gaeta  _et al._ (2019); Liu  _et al._ (2021), and can be designed
and manufactured to oscillate at any target frequency ranging from microwave
to millimeter-wave band Liang  _et al._ (2015a); Liu  _et al._ (2020a); Yao
_et al._ (2022); Tetsumoto  _et al._ (2021); Wang  _et al._ (2021). However, a
monolithic microcomb-based microwave oscillator requires photonic integration
of lasers, photodetectors and nonlinear microresonators on a common substrate,
which has still remained elusive. Here, we demonstrate the first of such a
fully integrated, microcomb-based, photonic microwave oscillator at 10.7 GHz.
The chip device, powered by a customized microelectronic circuit, leverages
hybrid integration of a high-power DFB laser, a Si3N4 microresonator of a
quality factor exceeding 25$\times$106, and a high-speed photodetector chip of
110 GHz bandwidth (3-dB) and 0.3 A/W responsivity. Each component represents
the state of the art of its own class, yet also allows large-volume
manufacturing with low cost using established CMOS foundries. The hybrid chip
outputs an ultralow-noise laser of 6.9 Hz intrinsic linewidth, a coherent
microcomb of 10.7 GHz repetition rate, and a 10.7 GHz microwave carrier of 6.3
mHz linewidth – all the three functions in one entity occupying a footprint of
only 76 mm2. The microwave phase noise reaches $-$75/$-$105/$-$130 dBc/Hz at
1/10/100 kHz Fourier offset frequency. Our results can reinvigorate our
information society for communication, sensing, imaging, timing and precision
measurement.

Introduction. Low-noise microwave oscillators are ubiquitously deployed in our
information society for communication, sensing, spectroscopy and timing. A
particularly important frequency band is the microwave X-band (8 to 12 GHz),
dedicated for radar, wireless networks, and satellite communication.
Currently, a paradigm shift is ongoing which utilizes photonics to synthesize
X-band microwaves Fortier  _et al._ (2011); Xie  _et al._ (2016); Li  _et al._
(2014); Liang  _et al._ (2015a); Liu  _et al._ (2020a); Yao  _et al._ (2022);
Li  _et al._ (2013a); Li and Vahala (2023); Tang  _et al._ (2018). Compared to
the electronic counterpart, the photonic microwave generation enables
unrivalled performance, particularly in noise and bandwidth.

Among all photonics-based approaches, optical frequency combs Cundiff and Ye
(2003); Fortier and Baumann (2019); Diddams  _et al._ (2020), which coherently
link radio- or microwave frequency to optical frequency, have enabled
microwaves with unrivalled spectral purity (noise) by leveraging optical
frequency division (OFD) Fortier  _et al._ (2011); Xie  _et al._ (2016); Li
_et al._ (2014). Optical-clock-referenced OFD Nakamura  _et al._ (2020) has
created 10 GHz microwaves with $10^{-16}$ fractional frequency instability at
1 s, two orders of magnitude more stable than the cesium fountain clocks
defining the SI second. Currently, by virtue of high-$Q$ optical
microresonators and harnessing the Kerr nonlinearity, an emerging paradigm is
to develop and apply microresonator-based Kerr frequency combs, i.e.
“microcombs” Kippenberg  _et al._ (2018); Pasquazi  _et al._ (2018); Herr  _et
al._ (2013); Yi  _et al._ (2015); Brasch  _et al._ (2016); Joshi  _et al._
(2016); Xue  _et al._ (2015) that have small size, weight and power
consumption. In particular, exploiting recent breakthroughs in fabrication of
ultralow-loss photonic integrated circuits (PIC) Moss  _et al._ (2013); Gaeta
_et al._ (2019); Liu  _et al._ (2021), optical microresonators can now be
constructed on a plethora of integrated material platforms Kovach  _et al._
(2020); Chang  _et al._ (2022). These PIC-based microresonators have permitted
chip-level microcombs with diverse merits and functions. Notably, latest
endeavors have demonstrated microcomb-based OFD Kudelin  _et al._ (2023); Sun
_et al._ (2023); Jin  _et al._ (2024); He  _et al._ (2024). Despite, these OFD
setups are still bulky, and require sophisticated locking techniques and
external references. Therefore, a free-running microcomb-based microwave
oscillator that is fully integrated at chip scale is still beneficial, though
the phase noise can be compromised.

Figure 1:  Schematic and images of the hybrid, microcomb-based, photonic
microwave oscillator. a. Schematic of the chip device. The microelectronic
circuit supplies current to the DFB laser and stabilizes its temperature. Via
edge-coupling, the CW light from the laser enters the Si3N4 microresonator
($A^{+}$). Exploiting the optical back-scattering ($A^{-}$) from the Si3N4
microresonator to the laser, laser self-injection locking occurs that
significantly narrows the laser linewidth. Simultaneously a circulating
platicon/dark-pulse stream is formed in the microresonator. The output pulse
stream is received by the PD chip that outputs a microwave carrier at the
pulse repetition rate. $S_{\phi}$, microwave phase noise. $f_{\text{offset}}$,
Fourier offset frequency. b. Photo of the hybrid chip device and individual
components. c. Zoom-in image showing the DFB laser wire-bonded to a PCB and
edge-coupled to the Si3N4 microresonator chip. d. Zoom-in image showing the
the PD chip edge-coupled to the Si3N4 chip and connected by a ground-source-
ground (GSG) probe for microwave signal output. e. False-colored SEM image
showing PD’s multilayer structure. InGaAs, indium gallium arsenide. InGaAsP,
Indium gallium arsenide phosphide. InP, Indium phosphide. BCB,
benzocyclobutene, a kind of resin.

Here, we demonstrate the first fully integrated, microcomb-based, photonic
microwave oscillator. The chip device leverages hybrid integration Stern  _et
al._ (2018); Raja  _et al._ (2019); Shen  _et al._ (2020) of a distributed-
feedback (DFB) laser chip, a high-$Q$ silicon nitride (Si3N4) microresonator
chip, and a photodetector (PD) chip. The schematic and components are depicted
in Fig. 1. The DFB laser chip is driven and stabilized by a microelectronic
circuit, and emits CW light at 1550 nm. Via edge-coupling, the light enters
the Si3N4 microresonator of 10.7 GHz free spectral range (FSR), where a
coherent platicon microcomb of 10.7 GHz repetition rate is formed. The output
light from the Si3N4 microresonator is delivered to the PD chip. Upon
photodetection of the microcomb’s repetition rate Liang  _et al._ (2015a); Liu
_et al._ (2020a); Yao  _et al._ (2022), the PD outputs a microwave carrier of
10.7 GHz and its harmonics. The entire device occupies a footprint of only 76
mm2.

## Characterization of individual components

Laser. We use a commercial DFB laser as shown in Fig. 1b,c. The laser outputs
160 mW CW light at 1549.9 nm with 500 mA laser current. The free-running DFB
laser exhibits 55 mA current at laser threshold, transverse-electric (TE)
polarization, and 1 nm wavelength tunability over a laser current up to 500
mA. The laser’s temperature is stabilized at 30∘C using a thermo-electric
cooler (TEC). A printed circuit board (PCB) provides driving current and
temperature stabilization to the laser chip. The laser chip is edge-coupled to
the Si3N4 chip Raja  _et al._ (2019); Shen  _et al._ (2020); Lihachev  _et
al._ (2022). The laser output waveguide is aligned to the inverse taper of the
Si3N4 bus waveguide and side-coupled to the microresonator. The coupling
efficiency between the laser chip and the Si3N4 chip is measured as 23%, i.e.
with 6.4 dB insertion loss. Extra characterization data are shown in
Supplementary Information. This loss value can be reduced in the future using
optimized inverse taper that matches the laser output mode.

Microresonator. The Si3N4 chip contains a high-$Q$ microresonator of 10.7 GHz
FSR, as shown in Fig. 1b. A high $Q$ is critical for microcomb generation,
since the power threshold $P_{0}$ for Kerr parametric oscillation is
$P_{0}\propto 1/(D_{1}Q^{2})$, where $D_{1}/2\pi$ is the FSR Kippenberg  _et
al._ (2018); Pasquazi  _et al._ (2018). We fabricate Si3N4 waveguides of 300
nm thickness using a deep-ultraviolet (DUV) subtractive process on 150-mm-
diameter (6-inch) wafers Ye  _et al._ (2023). The optimized fabrication
process is described in Supplementary Information. We choose 300 nm Si3N4
thickness for the following reasons. First, since high-quality Si3N4 films
deposited via low-pressure chemical vapor deposition (LPCVD, as used in our
case) are prone to crack due to intrinsic tensile stress Luke  _et al._
(2013), Si3N4 films with thickness below 300 nm are free from cracks. Second,
300-nm-thick Si3N4 fabrication process is currently established as a standard
process in nearly all CMOS foundries worldwide Muñoz  _et al._ (2019); Xiang
_et al._ (2022).

We characterize 70,220 resonances in the fundamental transverse-electric
(TE00) mode from 27 chips uniformly distributed over the 6-inch wafer, using a
vector spectrum analyzer Luo  _et al._ (2023) covering 1480 to 1640 nm (see
Method). The waveguide width of the Si3N4 microresonator is 2.6 $\mu$m. Each
resonance’s intrinsic linewidth $\kappa_{0}/2\pi$ and central frequency
$\omega/2\pi$ are measured and fitted. The histogram of intrinsic quality
factors $Q_{0}=\omega/\kappa_{0}$ of the 70,220 resonances is shown in Fig.
2a. The most probable value is $Q_{0}=25\times 10^{6}$, corresponding to a
linear optical loss of $\alpha\approx 1.3$ dB/m (physical length). Figure 2c
shows the measured $Q_{0}$ distribution over the entire wafer, where
$Q_{0}\geq 20\times 10^{6}$ is found in most places. Such a high $Q$ value is
sufficient for coherent microcomb generation in the Si3N4 microresonator with
37.7 mW power in the bus waveguide.

There are two types of coherent microcombs, i.e. the bright dissipative Kerr
soliton (DKS) Herr  _et al._ (2013); Yi  _et al._ (2015); Brasch  _et al._
(2016); Joshi  _et al._ (2016); Liang  _et al._ (2015a), and the dark pulse or
platicon Xue  _et al._ (2015); Lobanov  _et al._ (2015); Huang  _et al._
(2015); Parra-Rivas  _et al._ (2016); Nazemosadat  _et al._ (2021). Figure 2b
shows the measured microresonator’s integrated dispersion $D_{\text{int}}$
(see definition in Method). Our Si3N4 microresonator features normal group
velocity dispersion (GVD, $D_{2}<0$), permitting platicon generation. In
contrast, DKS requires anomalous GVD ($D_{2}>0$) that necessitates Si3N4
thickness above 600 nm and specific dispersion engineering Okawachi  _et al._
(2014); Luke  _et al._ (2013).

In addition, we emphasize another two advantages of using platicons instead of
DKS for microwave generation. First, compared to DKS, platicons exhibit
remarkably higher CW-to-pulse power conversion efficiency Xue  _et al._
(2017); Jang  _et al._ (2021). For 10.7 GHz repetition rate, we achieve $8\%$
power conversion efficiency using platicons (discussed later), while the
typical value is $\sim 0.2\%$ for DKS Liu  _et al._ (2020a); Jang  _et al._
(2021). Second, for DKS-based microwave generation, the CW pump must be
filtered or blocked before photodetection of the pulse’s repetition rate Liang
_et al._ (2015a); Liu  _et al._ (2020a); Yao  _et al._ (2022). Otherwise, the
overwhelmingly strong pump can saturate the PD, yielding deteriorated power
and phase noise of the microwave signal. Therefore, a filtering element, e.g.
a notch filter, is required in the DKS-based microwave oscillator, which
however complicates the overall system and photonic integration. In contrast,
platicon-based microwave oscillator does not require such a filter, as in our
case. In fact, the presence of the strong CW pump is beneficial. The pump
beats against its two neighboring comb lines – with the highest power among
all comb lines – and generates strong microwave signal at the repetition rate.
In sum, we employ platicons for photonic microwave generation.

Figure 2:  Characterization of Si3N4 microresonators and the photodetector
chip. a. Histogram of 70,220 measured intrinsic quality factor $Q_{0}$ from
twenty-seven Si3N4 chips on a 6-inch wafer. The most probable value is
$Q_{0}=25\times 10^{6}$. b. Profile of microresonator’s integrated dispersion
$D_{\text{int}}/2\pi$ of the 10.7-GHz-FSR Si3N4 microresonator. Red dots are
measured data, and the blue line is the polynomial fit.
$\omega_{0}/2\pi=193.324$ THz is the reference frequency corresponding to the
pump DFB’s frequency. $D_{1}/2\pi=10.686$ GHz is the microresonator FSR.
$D_{2}/2\pi=-87.27$ kHz is the normal GVD. See Method for the definition of
$D_{\text{int}}$. c. The most probable values $Q_{0}$ of the Si3N4 chips at
different places uniformly across the 6-inch wafer. In most places $Q_{0}\geq
20\times 10^{6}$ values are found, showing high yield of the Si3N4 fabrication
process. NA, not available. d. Frequency response of the $3\times 15$
$\mu\text{m}^{2}$ PD chip. Red dots are measured data, and the blue line is
the polynomial fit. e. Measured dark current versus bias voltage of the PD
chip. Negative bias voltage leads to dark current below 1 nA. f. Measured
responsivity versus wavelength of the PD chip. g. RF power versus the AC
current of the PD chip. Measured data (red dots) is comparable with the ideal
case (black line).

Photodetector. The high-speed PD is edge-coupled to the Si3N4 chip’s output
waveguide, and is connected by a ground-source-ground (GSG) probe for
microwave signal output, as shown in Fig. 1d. The epitaxial structure of the
PD chip is grown on a semi-insulating indium phosphide (InP) substrate Li  _et
al._ (2023). Figure 1e shows the false-colored scanning electron microscope
(SEM) image of the PD’s cross-section and multi-layer structure. The
fabrication process of the PD chip starts with P-type contact metals
(Ti/Pt/Au/Ti) deposition. Dry etching steps are then performed using
inductively coupled plasma etching to form a triple-mesa structure. After the
deposition of N-type contact metals (GeAu/Ni/Au), a benzocyclobutene (BCB)
layer is implemented beneath the coplanar waveguides (CPWs). This approach
eliminates the necessity for air-bridge structures, thus ensuring a consistent
and stable connection between p-mesa and CPWs. Details of the fabrication
process are found in Supplementary Information.

The frequency response of the InGaAs/InP waveguide device is investigated by
an optical heterodyne setup. Upon receiving a heterodyne beatnote between two
tunable lasers with wavelengths near 1550 nm, the PD outputs a high-frequency
RF signal whose power is measured by a Rohde & Schwarz powermeter (NRP-Z58).
Details of the characterization setup are found in Ref. Li  _et al._ (2023). A
typical frequency response for $3\times 15$ $\mu$m2 PD chip is shown in Fig.
2d. By a polynomial fit of the measured data, 3-dB bandwidth over 110 GHz is
shown. The I-V characteristics of the $3\times 15$ $\mu$m2 PD chip are
measured by a semiconductor device analyzer. Figure 2e shows the measured dark
current below 1 nA, which out-performs commercial high-speed PDs. Figure 2f
shows the responsivity as high as 0.3 A/W and above 0.2 A/W within 152 nm
bandwidth. Figure 2g shows the voltage-dependent saturation property of the PD
measured around 10 GHz. The ideal relationship between RF power
$P_{\text{RF}}$ and DC photo-current $I_{\text{dc}}$ is
$P_{\text{RF}}=I_{\text{dc}}^{2}R_{\text{load}}/2$, assuming a 100% modulation
depth ($I_{\text{ac}}=I_{\text{dc}}$), where $R_{\text{load}}=50\ \Omega$ is
the load resistance and $I_{\text{ac}}$ is AC photo-current.

Figure 3:  Characterization of laser self-injection locking. a. Theoretical
model of SIL dynamics using our experimental parameters. The red/gray line
represents the steady-state solution with/without SIL. The vertical axis is
the frequency detuning between the SIL DFB laser to the microresonator’s
resonance. The top horizontal axis is the frequency detuning between the free-
running DFB laser to the microresonator’s resonance. The bottom horizontal
axis is the DFB current relative to $I_{0}$. The blue/green dashed line marks
the forward/backward tuning curves. b. Experimental setup. OSA, optical
spectrum analyser. ESA, electronic spectrum analyser. TC/CC,
temperature/current control. c. Measured SIL dynamics. The vertical axis is
the beat frequency $f$ between the reference laser and the SIL laser. In the
forward/backward tuning, the DFB current increases/decreases and thus the
laser frequency decreases/increases. Color bar marks the beat signal’s power.
The flat segments signal the occurrence of SIL. The multiple beat frequencies
($f_{1}$ to $f_{6}$ and $f_{r}$ to $3f_{r}$) signal platicon microcomb
generation. d. Illustration of the reasons for $f_{1}$ to $f_{6}$ and $f_{r}$
to $3f_{r}$. Upper panel shows the microresonator’s resonance grid. Lower
panel illustrates that, the microcomb’s lines (blue) beat with the reference
laser (red) and generate $f_{1}$ to $f_{6}$; the microcomb’s lines beat among
themselves and generate $f_{r}$, $2f_{r}$ and $3f_{r}$.  Figure 4:
Characterization of platicon microcombs and microwaves. a. Optical spectra of
the generated platicons with DFB current of 313.25 and 364.75 mA – the two SIL
regions in the backward tuning in Fig. 3c. b. Frequency noise spectra of the
free-running (blue) and SIL (red) DFB lasers. The frequency noise of the free-
running DFB laser is 1248 Hz2/Hz corresponding to 7.8 kHz intrinsic linewidth.
The SIL laser’s frequency noise reaches 1.1 Hz2/Hz corresponding to 6.9 Hz
intrinsic linewidth. Gray area marks the region below 1.6 Hz2/Hz corresponding
to 10 Hz intrinsic linewidth. Green data is the result in Ref.Jin  _et al._
(2021). c. Measured Allan deviations of the SIL laser (red) and the generated
10.7 GHz microwave (blue). d. Phase noise spectra of our 10.7 GHz microwave
(solid red line), the second harmonic (21.4 Ghz, dashed red line), and the
third harmonic (32.1 GHz, dashdot red line), in comparison with the spectra in
Ref.Jin  _et al._ (2021) (green line), Ref.Liu  _et al._ (2020a) (orange
line), and Ref.Lihachev  _et al._ (2022) (blue line), as well as the PNA floor
(light dashed blue line) and shot noise floor (dashed black line). While we
use an integrated PD chip, Ref.Jin  _et al._ (2021); Liu  _et al._ (2020a);
Lihachev  _et al._ (2022) use commercial, non-integrated PD via fiber
connection. Inset is the power spectrum of the 10.7 GHz microwave in our work.
RBW, resolution bandwidth.

## Experimental results

Narrow-linewidth laser and platicon microcomb. First, we characterize the
laser dynamics and platicon states with the PD chip removed. The free-running
DFB laser’s frequency is increased/decreased by decreasing/increasing the
laser driving current. By scanning the DFB current in the forward/backward
direction (increasing/decreasing the current) between 300 and 400 mA, the
laser frequency is tuned by 32.8 GHz, i.e. with tuning coefficient of $-0.328$
GHz/mA. When the laser frequency approaches a microresonator resonance, light
$A^{+}$ is coupled into the Si3N4 microresonator, as shown in Fig. 1a. Due to
surface roughness and bulk inhomogeneity of the Si3N4 waveguide, back-
scattered light $A^{-}$ is generated within the microresonator, and is
injected back into the laser without an optical isolator. This back-scattered
light can trigger laser self-injection locking (SIL) Liang  _et al._ (2015b);
Kondratiev  _et al._ (2017, 2023); Voloshin  _et al._ (2021), which locks the
laser frequency $\nu$ to the microresonator resonance, as shown in Fig. 3a
(see Supplementary Information). The locking range $\Delta\nu_{\text{lock}}$
is defined as Kondratiev  _et al._ (2017, 2023)

$\Delta\nu_{\text{lock}}\approx
2\nu\sqrt{1+\alpha_{\text{g}}^{2}}\frac{\eta\beta}{Q_{\text{d}}R_{\text{o}}}.$
(1)

where $\alpha_{\text{g}}$ is the phase-amplitude factor of the DFB laser,
$\eta=\kappa_{\text{ex}}/(\kappa_{\text{ex}}+\kappa_{0})$ is the coupling
efficiency with $\kappa_{\text{ex}}$ being the external coupling rate and
$\kappa_{0}$ being the intrinsic loss, $\beta$ is the coupling rate between
the counter-propagating modes ($A^{+}$ and $A^{-}$) in unit of $\kappa/2$ with
$\kappa=\kappa_{\text{ex}}+\kappa_{0}$, $Q_{\text{d}}$ is the DFB laser
cavity’s quality factor, $R_{\text{o}}$ is the reflectivity of the output
facet of the DFB laser.

Once SIL occurs, the intrinsic laser linewidth is significantly suppressed due
to the high quality factor $Q_{\text{m}}$ of the Si3N4 microresonator which is
much higher than $Q_{\text{d}}$ Liang  _et al._ (2015b); Kondratiev  _et al._
(2017, 2023). The suppression ratio of intrinsic laser linewidth can be
expresses as

$\frac{\delta\nu_{\text{lock}}}{\delta\nu_{\text{free}}}\approx\frac{Q_{\text{d}}^{2}}{Q_{\text{m}}^{2}}\frac{1}{64\eta^{2}\beta^{2}(1+\alpha_{\text{g}}^{2})},$
(2)

where $\delta\nu_{\text{lock}}$ is the locked laser’s intrinsic linewidth, and
$\delta\nu_{\text{free}}$ is the free-running laser’s intrinsic linewidth. In
addition, with sufficient intra-cavity optical power in the Kerr-nonlinear
Si3N4 microresonator, nonlinear SIL can lead to DKS Raja  _et al._ (2019);
Shen  _et al._ (2020); Voloshin  _et al._ (2021); Pavlov  _et al._ (2018) or
platicon formation Jin  _et al._ (2021); Lihachev  _et al._ (2022), depending
on the microresonator GVD. In our case with normal GVD, platicons are
generated.

The experimental setup to characterize nonlinear SIL dynamics and platicon
generation is shown in Fig. 3b. A tunable diode laser (Toptica CTL 1550) is
frequency-stabilized to a self-referenced fiber optical frequency comb
(Quantum CTek). It serves as a reference laser to beat against the DFB laser
emitted from the Si3N4 chip. The beat signal’s frequency $f$ is recorded by an
electronic spectrum analyser (ESA, Rohde & Schwarz FSW43), and the optical
spectrum is recorded by an optical spectrum analyser (OSA, Yokogawa AQ6370D).

As shown in Fig. 3c, while the beat frequency $f$ has a global monotonic
dependence on the DFB current, it also exhibits multiple flat segments that
stay nearly constant when the DFB current varies by less than 10 mA. For
example, in the backward tuning, $f$ is nearly constant from $\sim 372$ to
$\sim 363$ mA and from $\sim 320$ to $\sim 311$ mA. Such behaviors signal the
occurrence of SIL and platicon generation. Degrading SIL performance can be
resulted from the presence of the Si3N4 bus waveguide that serves as an extra
Fabry-Pérot cavity with weak reflection (see Supplementary information).

The multiple beat frequencies ($f_{1}$ to $f_{6}$) in Fig. 3c within the SIL
region, e.g. around 320 mA DFB current in the forward tuning, are illustrated
in Fig. 3d. Assuming that the pump laser frequency is close to the resonance
mode $N$. Then $f_{1}$ to $f_{6}$ are the beat frequencies between the
reference laser and the platicon’s comb lines including the pump. Meanwhile,
$f=m\cdot f_{r}$ ($m$ is an integer) is the beat frequencies among the comb
lines, where $f_{r}\approx 10.7$ GHz is the mode spacing (i.e. the platicon’s
repetition rate). As the DFB current is tuned to 372 mA in the forward tuning,
the laser frequency approaches the $N+1$ resonance mode, leading to another
SIL region. Identical behaviors are found in the backward tuning. Considering
both directions, the DFB current can be tuned by 12.3 mA in the SIL region,
corresponding to a full locking range about 4.0 GHz. Such nonlinear SIL
dynamics with platicon generation is similar to the dynamics with DKS
generation in Ref. Voloshin  _et al._ (2021).

The optical spectra of platicon states at 313.25 and 364.75 mA DFB current in
the backward tuning are shown in Fig. 4a. In the SIL region and with 313.25 mA
current, the output microcomb power excluding the pump line from the Si3N4
chip is about 1.1 mW. When the DFB laser frequency is off-resonant, the CW
output power from the Si3N4 chip is 14 mW. Therefore the CW-to-platicon
conversion efficiency is calculated as 8%. Figure 4b shows the optical
frequency noise of the SIL laser characterized by a delayed self-heterodyne
method Yuan  _et al._ (2022) (see Supplementary Information). The lowest
frequency noise is 1.1 Hz2/Hz, corresponding to 6.9 Hz intrinsic linewidth and
31-dB noise suppression on the free-running DFB laser.

Low-noise microwave. The demonstrated narrow linewidth and ultralow noise of
the SIL laser are critical for low-noise microwave generation, since the
microwave phase noise inherits the laser phase noise with a certain
transduction factor Liu  _et al._ (2020a); Tetsumoto  _et al._ (2021).
Finally, we edge-couple the PD chip to the Si3N4 chip, enabling photonic
microwave generation up to 110 GHz within the PD’s bandwidth. Microwave
carriers with frequencies corresponding to the platicon’s repetition rate of
$f_{r}\approx 10.7$ GHz and harmonics of $f_{r}$ are output. Here, we focus on
the 10.7 GHz microwave and its second (21.4 GHz in the K-band) and third
harmonics (32.1 GHz in the K${}_{\text{a}}$-band). The RF power exported from
the PD chip is $-28$/$-30$/$-33$ dBm for the 10.7/21.4/32.1 GHz microwave. The
10.7 GHz microwave’s power spectrum is shown in Fig. 4d inset with 6.3 mHz
measured linewidth. The microwave’s phase noise is measured with 20-times
averaging by a phase noise analyzer (PNA, Rohde & Schwarz FSWP50), as shown in
Fig. 4d. The 10.7 GHz microwave’s phase noise reaches $-75$/$-105$/$-130$
dBc/Hz at 1/10/100 kHz Fourier offset frequency. The phase noise of the
second-/third-harmonic microwave is about 6.0/9.5 dB higher, in agreement with
the scaling law of $20\log N$ ($N=2$ or $3$). In comparison, we plot the
results in Ref. Jin  _et al._ (2021); Lihachev  _et al._ (2022); Liu  _et al._
(2020a) which use commercial, non-integrated PDs via fiber connection. Figure
4c shows the Allan deviations of the SIL laser frequency and the microwave
frequency measured by the PNA. The resemblance in trend indicates that the
long term stability of the microwave is dominated by the SIL laser frequency.

## Conclusion

In conclusion, we have demonstrated a fully integrated photonic microwave
oscillator at 10.7 GHz using a platicon microcomb. Such a hybrid chip device,
occupying a footprint of only 76 mm2, consists of a high-power DFB laser, a
high-$Q$ Si3N4 microresonator, and a high-speed PD. Each component represents
the state of the art of its own class, yet can be manufactured in large volume
with low cost using established CMOS foundries of integrated photonics.

Leveraging laser self-injection locking, the laser frequency noise is
suppressed by 31 dB, yielding an intrinsic linewidth of 6.9 Hz and platicon
microcomb generation. The PD chip further outputs a 10.7 GHz microwave carrier
of 6.3 mHz linewidth, and harmonics of 10.7 GHz benefiting from the PD’s 110
GHz bandwidth. In the future, the long-term stability of the three-in-one –
hybrid laser, comb and microwave – can be improved by PDH-locking to an ultra-
stable cavity Guo  _et al._ (2022); Cheng  _et al._ (2023). Recent advances Yu
_et al._ (2020); Xiang  _et al._ (2021); Liu  _et al._ (2020b); Snigirev  _et
al._ (2023) in heterogeneous integration of III-V, Si3N4 and modulators open a
path towards chip devices of further reduced sizes, improved stability and
added frequency tunability. Up-shifting the microwave frequency, even into the
millimeter-wave band, can be simply realized with Si3N4 microresonators of
larger FSR Tetsumoto  _et al._ (2021); Wang  _et al._ (2021) and modified uni-
traveling-carrier (MUTC) InP PD chips Li  _et al._ (2023). Such low-noise
microwaves from hybrid photonic chips of small size, weight and power
consumption can reinvigorate our information technology and applications for
microwave photonics, terrestrial broadband, traffic control, tracking, analog-
to-digital conversion, wireless networks, space links, and electron
paramagnetic resonance spectroscopy.

Methods

Characterization of microresonator dispersion. We use a vector spectrum
analyser (VSA) Luo  _et al._ (2023) to measure the central frequency
$\omega/2\pi$ and loaded linewidth
$\kappa/2\pi=(\kappa_{0}+\kappa_{\text{ex}})/2\pi$ of each resonance within
1480 to 1640 nm. The intrinsic loss $\kappa_{0}$ and external coupling rate
$\kappa_{\text{ex}}$ can be fitted based on the resonance’s transmission
profile Gorodetsky  _et al._ (2000); Li  _et al._ (2013b), extinction ratio
Cai  _et al._ (2000) and phase response Luo  _et al._ (2023). The intrinsic
($Q_{0}$) and loaded ($Q_{\text{m}}$) quality factors of each resonance can be
calculated as $Q_{0}=\omega/\kappa_{0}$ and $Q_{\text{m}}=\omega/\kappa$. Due
to the presence of microresonator dispersion, the measured resonance grid
deviates from an equidistant grid. Thus the $\mu^{\text{th}}$ resonance
frequency $\omega_{\mu}$ can be written as

$\displaystyle\omega_{\mu}=$
$\displaystyle\omega_{0}+D_{1}\mu+D_{2}\mu^{2}/2+D_{3}\mu^{3}/6+...$ (3)
$\displaystyle=$ $\displaystyle\omega_{0}+D_{1}\mu+D_{\text{int}}$ (4)

where $\omega_{0}$ is the reference resonance frequency, $D_{1}/2\pi$ is the
microresonator FSR, $D_{2}$ describes the GVD, $D_{3}$ is higher-order
dispersion terms. With known $\omega_{\mu}$, $\omega_{0}$ and fitted $D_{1}$,
the microresonator’s integrated dispersion
$D_{\text{int}}=\omega_{\mu}-\omega_{0}-D_{1}\mu$ can be plotted.

Funding Information: J. Liu acknowledges support from the National Natural
Science Foundation of China (Grant No.12261131503), Shenzhen-Hong Kong
Cooperation Zone for Technology and Innovation (HZQB-KCZYB2020050), and from
the Guangdong Provincial Key Laboratory (2019B121203002). B. C. acknowledges
support from the National Natural Science Foundation of China (Grant No.
61975121). Z. C. and Y.-H. L. acknowledge support from the China Postdoctoral
Science Foundation (Grant No. 2023M731508 and 2022M721482).

Acknowledgments: We thank Zhongkai Wang and Rumin Cheng for assistance in the
experiment, Dengke Chen for assistance in data processing, Chengying Bao,
Jijun He and Hairun Guo for the fruitful discussion. The DFB lasers were
fabricated by Henan Shijia Photons Technology Co., Ltd and Shenzhen PhotonX
Technology Co. Ltd. Silicon nitride chips were fabricated by Qaleido
Photonics. The PD chips were fabricated with support from the ShanghaiTech
University Quantum Device Lab (SQDL).

Author contributions: W. S., Z. C., J. Long, H. Z. performed the experiment
with assistance from S. L.. The Si3N4 chips were fabricated by C. S. and L.
G., and characterized by B. S. and Y.-H. L.. The PD chips were fabricated by
L. L., L. W., Q. C. and B. C.. W. S., Z. C., Y.-H. L., B. C. and J. Liu wrote
the manuscript, with the input from others. J. Liu supervised the project.

Disclosures: W. S., Z. C., J. Long and J. Liu are inventors on a patent
application related to this work. C. S. and J. Liu are co-founders of Qaleido
Photonics, a start-up that is developing heterogeneous silicon nitride
integrated photonics technologies. Others declare no conflicts of interest.

Data Availability Statement: The code and data used to produce the plots
within this work will be released on the repository Zenodo upon publication of
this preprint.

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