# Engineered zero-dispersion microcombs using CMOS-ready photonics

Qing-Xin Ji1,∗, Warren Jin2,4∗, Lue Wu1,∗, Yan Yu1,∗, Zhiquan Yuan1, Wei
Zhang3, Maodong Gao1, Bohan Li1, Heming Wang1,2, Chao Xiang2, Joel Guo2, Avi
Feshali 4, Mario Paniccia 4, Vladimir S. Ilchenko3, Andrey B. Matsko3, John
Bowers2,† and Kerry Vahala1,†
1T. J. Watson Laboratory of Applied Physics, California Institute of
Technology, Pasadena, CA 91125, USA
2Department of Electrical and Computer Engineering, University of California,
Santa Barbara, Santa Barbara, CA 93106, USA
3Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove
Drive, Pasadena, CA 91109, USA
4Anello Photonics, Santa Clara, CA 95054, USA
∗These authors contributed equally to this work.
†Corresponding author<EMAIL_ADDRESS><EMAIL_ADDRESS>
Abstract

Normal group velocity dispersion (GVD) microcombs offer high comb line power
and high pumping efficiency compared to bright pulse microcombs. The recent
demonstration of normal GVD microcombs using CMOS-foundry-produced
microresonators is an important step towards scalable production. However, the
chromatic dispersion of CMOS devices is large and impairs generation of
broadband microcombs. Here, we report the development of a microresonator in
which GVD is reduced due to a couple-ring resonator configuration. Operating
in the turnkey self-injection-locking mode, the resonator is hybridly
integrated with a semiconductor laser pump to produce high-power-efficiency
combs spanning a bandwidth of 9.9 nm (1.22 THz) centered at 1560 nm,
corresponding to 62 comb lines. Fast, linear optical sampling of the comb
waveform is used to observe the rich set of near-zero GVD comb behaviors,
including soliton molecules, switching waves (platicons) and their hybrids.
Tuning of the 20 GHz repetition rate by electrical actuation enables servo
locking to a microwave reference, which simultaneously stabilizes the comb
repetition rate, offset frequency and temporal waveform. This hybridly
integrated system could be used in coherent communications or for ultra-stable
microwave signal generation by two-point optical frequency division.

Introduction

Fig. 1: Self-injection-locked zero-dispersion microcomb using a coupled-ring
resonator.  a, Photograph of the coupled ring resonators showing DFB pump
laser. The two rings are nearly degenerate ($FSR$ difference is $\sim 100$
MHz). b, Lower panel shows the coupled rings pumped by a DFB laser which is
self-injection locked to a resonator mode. Periodic pulse trains (light red
arrow) are generated. Upper panel shows the cross-sectional waveguide geometry
of the ring coupling region (2.8 $\mu$m wavegudie width and 2.4 $\mu$m
waveguide gap). c, Measured group velocity dispersion (GVD) parameter $D_{2}$
of the mode resonances versus wavelength. Zero dispersion is achieved near
$1542$ nm and $1559$ nm. d,  Optical spectra of the generated frequency comb
when pumped near the two zero dispersion points. For the comb pumped at 1541
nm (gray), the span is 9.2 nm (as marked by the arrows). For the comb pumped
at 1559 nm (orange), the span is 9.9 nm. The dashed line indicates the
estimated on-chip line power of 1 $\mu$W. e, f,  Measured microwave frequency
spectrum of the detected microcomb output when pumped at 1542nm (e) and 1560
nm (f). The resolution bandwidth is 10 kHz.  Fig. 2: Microcomb optical spectra
and temporal waveforms measured at specific pumping wavelengths near the zero
GVD wavelength. a, Solid lines give the integrated dispersion, defined as
$D_{\rm int}=\omega_{\mu}-\omega_{0}-D_{1}\mu$ (right-hand side of Eqn. 1),
measured at pumping wavelengths shown in the legend. The colored dashed lines
denote the comb line frequencies (left-hand side of Eqn. 1) when pumped at the
specified pumping wavelengths. The intersection of the mode resonances (solid
line) and comb lines (dashed line) generates a dispersive wave. b, Measured
GVD parameter $D_{2}$ versus wavelength near the zero GVD point. Arrows
correspond to the pump wavelengths shown in panel a. Errorbar denotes standard
deviation from the third-order polynomial fitting. c-f, Left panels: optical
spectra of the microcomb when pumped near the zero-dispersion wavelength
(specific pumping wavelength indicated and correspond to values in panel a).
Simulated optical spectrum is plotted as the dashed black curve. The
dispersive wave position from panel a is marked by arrows. Right panel:
measured microcomb temporal waveform during one round trip for the pumping
wavelength given in left panel.  Fig. 3: Discipline of the SIL microcomb
repetition rate to an external microwave reference.  a, Experimental setup for
external disciplining of the SIL microcomb repetition rate. PZT: Piezo-
electric transducer. PD: photo detector. Servo: laser servo. Inset: schematic
view of laser detuning $\delta\omega$ stabilization via repetition rate
discipline. Fluctuation in $\delta\omega$ leads to fluctuation in repetition
rate $\delta\omega_{\rm rep}$, which is measured and compared to a microwave
reference to generate the error signal for feedback to the laser driving
current. Frequency noise of the free-running DFB laser (gray) is reduced by
SIL (blue) and then reduced further by repetition rate locking (red). b,
Repetition rate phase noise and microwave spectra of the free-running SIL
microcomb (blue) and the externally disciplined microcomb (red). Measured
phase noise of the microwave reference is plotted in gray. c, Repetition rate
tuning of the external disciplined microcomb. Measured microwave tone of the
comb is plotted in different colors. The resolution bandwidth is 100 Hz. d,
Stability of temporal waveform of the microcomb under free-running SIL (left)
and external discipline (right). In the right panel, two dashed white lines
give the linear motion of the waveform in the fast frame.  Fig. 4: Optical
frequency noise of the pump laser (comb offset frequency).  Grey curve gives
the free-running (non SIL) measurement, blue curve is for self injection
locked (SIL) operation, and the red curve is for repetition rate discipline
using an external microwave reference. The thermorefractive noise floor is
denoted by the dashed gray line.

Soliton mode locking in optical microresonators 1 is receiving intense
interest for chip-scale integration of frequency comb systems 2, 3, 4. An
important advancement has been the realization of microcombs that are directly
pumped by semiconductor lasers without amplification 5, 6, 7, 8. These systems
have resulted from steady progress in boosting of resonator $Q$ factor so as
to lower pumping power, especially in detectable-rate microcombs 9, 10, 11,
12, 13, 14, 7. The directly pumped sytems benefit from self-injection-locking
(SIL) of the pump by feedback from the microcomb resonator 15, 16. SIL
operation simplifies integration by eliminating the optical isolator component
between pump and microcomb, and it also narrows the pump line. Critically, it
has also been shown that SIL tends to simplify the soliton turn-on process,
making it deterministic (or turnkey) for bright solitons 6.

Normal GVD dispersion microcombs 17 have also been shown to benefit from SIL
operation 7, 18, 19. Not only does the pulse triggering become deterministic,
but switching-wave stability dynamics that normally favor large or very small
duty cycles, are overcome and pulse duty cycle lies closer to the ideal 50$\%$
for maximal comb power and efficiency18. This is advantageous for microwave
generation as well as for use of the microcomb as a WDM communications source
20. Despite these useful properties of the normal GVD SIL microcombs, the
spectral width of these systems is limited. For example, in high-$Q$ CMOS-
ready resonators, comb lines extend to about 4 nm due to the strong normal
chromatic dispersion of the low-confinement waveguides 7, 21. An intriguing
approach to extend bandwidth has been to drive microcombs near the zero GVD
wavelength where pulse formation is influenced by higher-order dispersion 22,
23, 24. Besides permitting a range of new pulse behaviors as the system is
operated above, below, or near the zero-dispersion wavelength, flattening in
the dispersion spectrum is generally possible, which broadens the comb span.
Under pulsed pumped operation near octave span detectable repetition rates
have been possible 22.

Here, dual coupled-ring (CR) resonators are used to produce near-zero-GVD
microcombs using the normal dispersion CMOS-ready platform. While prior zero-
GVD systems have used pulse pumping or optical amplification of continuous-
wave sources, the CR resonators feature high intrinsic $Q$ factors over 100
million (the highest of any CR resonator system), enabling SIL operation of
the microcombs with a heterogeneously-integrated III-V laser. This is also the
first application of the SIL mode of operation to zero-GVD on-chip systems and
it is observed to provide the turnkey benefit previously observed for
anomalous and normal dispersion systems, including high efficiency comb
operation 18. Comb bandwidth up to 9.9 nm (1.22 THz) is set by design for
application in a two-point optical frequency division system 25, 26. This
significantly improves upon prior CMOS-ready designs and also offers high comb
line powers required in the division system. To our knowledge, the number of
combs lines generated is a record for non-amplified and non-pulse-pumped zero-
GVD systems. The precise stepper-lithography-defined geometry of the CMOS-
ready system also enables good control of the zero-GVD wavelength. By tuning
the pumping laser near the zero-dispersion point, various mode-locked comb
states at microwave rates are observed. And by utilizing the linear optical
sampling technique assisted with an electro-optic frequency comb 27, the
temporal profiles of these states are measured for the first time including
soliton molecules 22, 23, switching waves 19, 18 and their hybrids 22.
Numerical modeling is in agreement with the optical spectra as well as the
measured temporal profiles. Servo locking of the microcomb repetition rate to
a microwave reference is also demonstrated and stabilized the comb repetition
rate, offset frequency and temporal waveform.

##  I High-$Q$ CMOS coupled ring system

In the experiment, high-$Q$ silicon nitride (SiN) coupled rings are fabricated
using the CMOS-ready process 7 (Fig. 1a). The silicon nitride layer thickness
is chosen as 100 nm to maintain single mode propagation while also boosting
$Q$ factor 7. Intrinsic $Q$ factors over 100 million are achieved
(Supplementary Note 1). The resonators are overcoupled with two bus waveguides
(Fig. 1a,b) to enhance comb efficiency (loaded $Q$ factor is $26$ million).
The uncoupled resonators feature normal dispersion and will generate dark
pulse combs when operated in the SIL configuration. Strong resonator coupling
is introduced to lower the dispersion, creating two zero GVD wavelengths
(around 1542 and 1559 nm) as shown in Fig. 1c. A discussion on repeatability
of dispersion between different devices is included in Supplementary Note 5.

Coupled ring resonators 28 offer a convenient way to engineer anomalous
dispersion into systems comprised of normal dispersion waveguides 29, 30. And
recently they have been studied in the context of normal GVD solitons to
engineer either zero-GVD 22 or controlled (as opposed to accidental 17)
avoided mode crossing through hybridization of a single mode pair in a
photonic molecule 31. Here, this hybridization is engineered to be broadband
so as to spectrally flatten the dispersion curve and make higher-order
dispersion important. This is done by first introducing strong mutual coupling
of rings wherein nearly 40% of mode power is coupled between resonators, and
second by close matching of the ring free-spectral range (FSR) values (the FSR
difference is 100 MHz on FSRs close to 20 GHz). The $Q$ factors of the coupled
rings are also much higher, enabling both detectable-rate comb operation and
hybrid integration with a III-V pump.

##  II Dispersion and SIL microcomb spectra

In the measurement, a DFB laser operating in the vicinity of one of the two
zero-dispersion wavelengths is butt-coupled to the resonator with $\sim 30-40$
mW power coupled onto the waveguide (Fig. 1a,b). Rayleigh scattering inside
the resonator reflects $\sim 2\%$ of the power into the pumping laser. An
Emcore Corp. DFB laser is used for pumping near 1559 nm and a PhotonX Inc. DFB
laser is used for pumping near 1541 nm. Temperature tuning of the DFB lasers
allows fine tuning control of the pumping wavelength for access to slightly
anomalous, near-zero, and slightly normal dispersion wavelengths of the
resonator. Fig. 2a shows measurements of integrated dispersion of the
resonator for pumping at specific wavelengths (provided in the legend) near
1559 nm. In the plots, $\mu=0$ corresponds to the pump line. The dispersion
curves are measured using a radio-frequency calibrated interferometer
reference 10.

When pumped at near-zero dispersion, the comb spectral span is strongly
influenced by comb radiation into a dispersive wave, which corresponds to
cavity modes that are nearly resonant with comb lines. The mode number
$\mu_{\rm dw}$ of the dispersive wave is given as the solution to the equation
32,

$-\delta\omega+2gP_{0}+\delta\omega_{\rm rep}\mu_{\rm
dw}=\frac{D_{2}}{2}\mu_{\rm dw}^{2}+\frac{D_{3}}{6}\mu_{\rm dw}^{3},$ (1)

where $\delta\omega$ is the pump-laser cavity detuning as regulated by the
self-injection feedback, $g$ is Kerr nonlinear coefficient, $P_{0}$ is photon
number of the pumped cavity resonance, $\delta\omega_{\rm rep}$ is the
difference between comb repetition rate and cavity free-spectral range
($D_{1}$), and $D_{2}$ and $D_{3}$ are second- and third-order dispersion
parameters, respectively. Fig. 2b gives the measured second-order dispersion
($D_{2}$) parameter at these same pumping wavelengths, and $D_{3}=7.5$ kHz is
used for all pumping wavelengths. The left side of Eqn. 1 corresponds to the
frequency comb lines and is plotted as the colored dashed lines in Fig. 2a. In
making these these line plots, $\delta\omega$ and $\delta\omega_{\rm rep}$ are
numerically simulated (Supplementary Note 4). The right side of Eqn. 1 is the
integrated dispersion and fitted to the experimentally measured dispersion as
noted above. At each pumping wavelength, the dispersive wave mode number
$\mu_{\rm dw}$ can be obtained as the intercept between the comb frequencies
(dashed lines) and the corresponding integrated dispersion curve (solid
lines).

The dispersive wave position is marked with an arrow in the left panel of Fig.
2 c-f, which show measured spectra for SIL pumping at the wavelengths in Fig.
2a. The arrow position provides a trend of measured comb span for negative
mode numbers. Overall comb spectral span tends to be determined by this
dispersive wave. Note that in Fig. 2, the third dispersive wave (after mode
number $\sim$50) is absent in both the measured and simulated optical
spectrum, which is a result of insufficient pump power. The comb spectrum in
Fig. 1d spans 9.9 nm (1.22 THz) and features on-chip comb-line power higher
than 1 $\mu$W, marked with arrows. This comb has superior spectral coverage
compared to previous SIL operated normal GVD microcombs 7, 19. It also
features an increased number of comb lines compared with higher repetition
rate non-bright combs directly III-V pumped with optical isolation 33. When
pumped at 1541 nm near the other zero-dispersion wavelength, a microcomb
spanning 9.2 nm (1.16 THz) is realized. The comb states both feature pump
power conversion efficiency as high as 26% (see Supplementary Note 2). These
comb spectra are plotted in Fig. 1d.

##  III Imaging of mode-locked microcomb states

While the temporal envelope of pulses produced by normal GVD combs has been
measured using cross-correlation 17, near-zero-GVD operation allows access to
a wider variety of comb states including soliton molecules (bounded bright
solitons) and switching waves 34, 32. These interesting states have been
analyzed numerically 35, 36, 22, but they have so far not been observed in the
time domain. This is result of current zero-dispersion systems being generated
with a pulsed pump where the comb waveform is influenced by the pump pulse
waveform or at challenging high repetition rates 37, 23, 38. Here, the linear
optical sampling technique assisted with an electro-optic frequency comb is
implemented to image the temporal profile of the various comb states 27, 18.
The sampling EO comb spans $\sim 5$ nm with 33 lines, corresponding to a $\sim
1.5$ ps pulse in the time domain, and its repetition rate is set to be
slightly higher than the zero-dispersion microcomb. Note that the temporal
duration of the soliton pulse (for example, 2.6 ps FWHM in Fig.2d for the left
pulse in measurement) is close to the pulse width of the EO-comb ($\sim$ 1.5
ps), thus the imaging result may not perfectly resolve fine structure in the
temporal waveforms. By combining the EO comb and the generated comb at the
“drop” port, and detecting with a fast photodetector, the sampled microcomb
signal is recorded by an oscilloscope for processing.

Experimental results are presented in the right panels of Fig, 2c,d,e,f. At
the anomalous side ($D_{2}>0$) of the near-zero GVD wavelength, the strong
dispersive wave binds several solitons into soliton clusters, as observed in
Fig.2c (right panel). The interference between the pulses creates the multiple
fringes that are apparent in the optical spectrum (left panel). Numerically
simulated time domain and spectra are also presented as dashed curves in Fig,
2c,d,e,f. The clustered soliton formation is preserved for near-vanishing GVD
($D_{2}/2\pi=-1.5$ kHz) as shown in Fig, 2d, where a soliton dimer is imaged.
The corresponding optical spectrum is shown in the left panel of Fig. 2d. For
the pumping wavelength with normal dispersion, the resulting waveforms are
often called switching waves or “platicons” 19, 18. Here, the waveform evolves
towards a square pulse as the dispersion becomes more normal ($D_{2}<0$) (Fig.
2e-f, right panels). The present results experimentally demonstrate the
evolution of comb states in the near zero GVD regime with different GVD sign,
and are consistent with a previous numerical study 22.

Generally, operation of the comb with a small amount of normal dispersion
(e.g. the state in Fig. 2e, pumped at 1559.2 nm) provides both good spectral
coverage as well as a temporal and spectral waveform that is more regular in
shape. Furthermore, the square pulse nature of these states (apparent in Fig.
2e-f, right panels) offers an increased duty cycle, which boosts comb power
conversion efficiency. As a result, the microwave and optical performance of
the comb state in Fig. 2e is further studied below.

##  IV Discipline of the comb repetition rate

Discipline of comb repetition rate to an external reference such as a clock is
important in many comb applications 3. Generally, the repetition rate of
microcombs is regulated by the pump-laser cavity detuning $\delta\omega$ 39,
40, via channels including dispersive wave recoil 39, Raman self-frequency
shift 41 and inhomogeneous back scattering 18, 42. And with laser cavity
detuning $\delta\omega$ controlled by the applied current on the pumping DFB
laser, a fast feedback loop can be used to stabilize the microcomb’s
repetition rate.

In the experiment (Fig. 3a), the microcomb’s repetition rate is detected at
the resonator drop port by a fast photo detector, and analyzed by a signal
analyzer (R&S FSUP). Pumping is at 1559.22 nm. The detected repetition rate
tone is simultaneously split by a directional coupler after electrical
amplification and mixed with a local oscillator which serves as the reference
(R&S SMB 100A). The mixed-down signal is sent to a servo controller and fed
back to the current supply (LDX-3620B, DC-coupled modulation response
bandwidth $<$1 MHz) of the DFB laser to provide fine tuning control of the
pump-laser cavity detuning frequency. The gap distance between the bus
waveguide facet and the DFB laser head is regulated by a closed loop piezo
(PZT) with a built-in strain gauge displacement sensor (Thorlabs MAX311D).

The measured phase noise of the detected repetition rate tone under open-loop
and disciplined (locked) conditions is shown in Fig. 3b. The phase noise of
the microwave reference is shown in gray. The phase noise of the disciplined
repetition rate follows that of the microwave reference within the feedback
bandwidth of approximately $100$ kHz (as defined by the offset frequency where
a “bump” is observed in its frequency spectrum). The microwave spectra of the
SIL and disciplined comb are plotted in inset of Fig. 3b. The repetition rate
could be tuned by 60 kHz through tuning of the microwave reference (Fig. 3c).
Disciplining the microcomb simultaneously stabilizes its temporal waveform.
This is observable in Fig. 3d which shows round trip comb field plotted versus
time. In the left panel the data are presented under unlocked conditions and
show drift of the soliton waveform over a time scale of 1 ms. On the other
hand, the disciplined microcomb features a measured soliton waveform that
evolves very slowly and linearly (linear trend lines shown as white dashed
lines). Here, the observable drift results from the difference in sampling
period between the oscilloscope and EO sampling signal. All of the sampling
data presented in Fig. 2 were obtained when the comb was externally
disciplined.

##  V Comb offset frequency stabilization under repetition rate discipline

The pump laser frequency of the microcomb also determines the offset frequency
of the microcomb. And self-injection locking (here of the pump laser) is known
to improve frequency stability 43. In the present case, SIL stabilizes the DFB
pump laser’s frequency to the high-$Q$ silicon nitride cavity mode and thereby
stabilizes laser-cavity detuning ${\delta\omega}$ to a value that depends on
the feedback phase and initial laser-cavity detuning without SIL feedback. The
pump laser frequency noise under SIL and free-running operation is measured in
Fig. 4. The measurement is performed by amplifying the microcomb output at the
drop port with an erbium-dope amplifier (EDFA) and filtering out the pump line
with a waveshaper. Frequency noise of the line is then measured with a cross-
correlation-based self-heterodyne measurement 44 within the measurement time
of 400 ms. Compared with the free running DFB laser (gray), frequency noise of
the pump laser is reduced by 30 dB under SIL operation (blue) at 10 kHz offset
frequency. An integrated linewidth $\Delta\nu_{\rm c}$ of 7.2 kHz is obtained
($\Delta\nu_{\rm
c}\equiv\int_{\Delta\nu_{c}}^{+\infty}S_{\delta\omega}(f)/f^{2}\mathrm{d}f=\frac{1}{2\pi}$).
The frequency noise here is still higher than the thermal noise limit given by
the dashed gray curve in Fig. 4 45 (see Supplementary Note 1).

Fluctuation of a microcomb’s repetition rate $\delta\omega_{\rm rep}$ is
largely controlled by the pump laser-cavity detuning ${\delta\omega}$ 19, 42.
As schematically illustrated in the inset of Fig. 3a, disciplining the
microcomb’s repetition rate thus simultaneously disciplines the laser pumping
frequency frequency relative to the pumped cavity resonance. With fluctuation
in ${\delta\omega}$ greatly reduced by disciplining the repetition rate,
frequency noise of the pump laser frequency (and comb offset frequency) is
further stabilized to the thermo-refractive noise limit, as plotted in red in
Fig. 4. The bumps at 1 kHz and 2 kHz originate from the piezo-electric motor
used to control the gap between the DFB laser head and the photonic chip. In
principle, heterogeneous integration or butterfly packaging6 of the pump and
the resonator would eliminate the need for this servo control or at least
replace it with a potentially faster equivalent control. It is noted that comb
offset noise at lower offset frequencies than the measurement in Fig.4 is
generally possible from (but not limited to) the ambient including temperature
fluctuations and mechanical vibrations, other than the noise sources noted
above 46. With the same definition as above, the calculated integrated
linewidth is 2.1 kHz, which is comparable to an ECDL pumped microcomb 47.

##  VI Summary

We have demonstrated a microwave-rate mode-locked microcomb near zero GVD
using a CMOS-ready coupled ring resonators. The reduced GVD enables broader
microcomb operation using integrated photonics with high conversion
efficiency, while maintaining the benefits of the self-injection feedback,
including turnkey operation and optical linewidth reduction. A record number
of comb lines is generated for non-amplified and non-pulse-pumped operation of
a normal dispersion microcomb. The dispersion engineering scheme in this paper
can be extended to other wavelengths and different photonic platforms.
Disciplining the microcomb to an external microwave reference simultaneously
stabilizes its microwave tone, temporal waveform and optical frequency. The
external discipline for the hybrid-integrated microcomb source demonstrated
here can be used in a two-point optical frequency division system 26 for low-
noise microwave synthesis.

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Funding. Defense Advanced Research Project Agency GRYPHON (HR0011-22-2-0009)
and APHI (FA9453-19-C-0029) programs; NASA.

Acknowledgments. The authors thank H. Blauvelt at EMCORE Corporation for
supplying the DFB laser used in this study, as well as N. Kondratiev and V.
Lobanov for discussions on numerical modelings. The authors also thank S.
Diddams and F. Quinlan for fruitful comments on the results. The reported here
research performed by W. Z., V.S.I. and A.B.M. was carried out at the Jet
Propulsion Laboratory, California Institute of Technology, under a contract
with the National Aeronautics and Space Administration (80NM0018D0004).

Disclosures. The authors declare no conflicts of interest.