Nature | www.nature.com |
1
Article
Photonic chip-based low-noise microwave
oscillator
Igor Kudelin
1,2
✉
, William
Groman
1,2
, Qing-Xin
Ji
3
, Joel
Guo
4
, Megan L. Kelleher
1,2
,
Dahyeon Lee
1,2
, Takuma
Nakamura
1,2
, Charles A. McLemore
1,2
, Pedram
Shirmohammadi
5
,
Samin Hanifi
5
, Haotian
Cheng
6
, Naijun
Jin
6
, Lue
Wu
3
, Samuel
Halladay
6
, Yizhi
Luo
6
,
Zhaowei Dai
6
, Warren
Jin
4
, Junwu
Bai
5
, Yifan
Liu
1,2
, Wei
Zhang
7
, Chao
Xiang
4
, Lin
Chang
4
,
Vladimir Iltchenko
7
, Owen
Miller
6
, Andrey
Matsko
7
, Steven M. Bowers
5
, Peter T. Rakich
6
,
Joe C. Campbell
5
, John E. Bowers
4
, Kerry J. Vahala
3
, Franklyn
Quinlan
1,8
&
Scott A. Diddams
1,2,8
✉
Numerous modern technologies are reliant on the low-phase noise and exquisite
timing stability of microwave signals. Substantial progress has been made in the field
of microwave photonics, whereby low-noise microwave signals are generated by the
down-conversion of ultrastable optical references using a frequency comb
1
–
3
. Such
systems, however, are constructed with bulk or fibre optics and are difficult to further
reduce in size and power consumption. In this work we address this challenge by
leveraging advances in integrated photonics to demonstrate low-noise microwave
generation via two-point optical frequency division
4
,
5
. Narrow-linewidth
self-injection-locked integrated lasers
6
,
7
are stabilized to a miniature Fabry–Pérot
cavity
8
, and the frequency gap between the lasers is divided with an efficient dark
soliton frequency comb
9
. The stabilized output of the microcomb is photodetected
to produce a microwave signal at 20 GHz with phase noise of −96 dBc Hz
−1
at 100 Hz
offset frequency that decreases to −135 dBc Hz
−1
at 10 kHz offset—values that are
unprecedented for an integrated photonic system. All photonic components can be
heterogeneously integrated on a single chip, providing a significant advance for the
application of photonics to high-precision navigation, communication and timing
systems.
Low-noise microwave signals with high timing stability are a critical
enabler of modern science and multiple technologies of broad soci-
etal impact. Positioning and navigation, advanced communications,
high-fidelity radar and sensing, and high-performance atomic clocks
are all dependent upon low-phase-noise microwave signals. These
rapidly developing technologies are constantly intensifying the
demand for microwave sources beyond current capabilities while
imposing harsher restrictions on system size, weight, and power
consumption (SWaP). In this landscape, photonic lightwave systems
provide unique advantages over more conventional electronic
approaches for generating low-noise microwaves. In particular, the
extremely low-loss and high-quality factors of photonic resonators
are fundamental to electromagnetic oscillators with the lowest noise
and highest spectral purity
10
. Coupled to this is the introduction and
rapid development of frequency combs in the last few decades that
enable seamless coherent synthesis across the full electromagnetic
spectrum
11
. This includes the frequency division of a 200–500 THz
optical carrier down to a 10 GHz microwave with unrivalled long- and
short-term stability
1
–
3
,
12
.
However, a significant challenge of these approaches is the relatively
large size and power consumption that restrict their use to laboratory
environments. Greater impact and widespread use can be realized
with a low-noise microwave generator that has a compact and port
-
able form factor for operation in remote and mobile platforms. Our
work addresses and overcomes this challenge through the optimal
implementation of two-point optical frequency division (2P-OFD) with
integrated photonic components as illustrated in Fig.
1
. We provide a
means to significantly reduce microwave phase noise in a volume of
tens of millilitres instead of tens of litres while similarly reducing the
required power by a factor 10
3
to the 1 W level.
All optical frequency division (OFD) systems start with a stable optical
frequency reference. Typically, this is a laboratory fibre or solid-state
laser that is frequency stabilized to a large evacuated Fabry–Pérot (F-P)
cavity
10
,
13
. Instead, we introduce an optimal combination of low-noise
chip-integrated semiconductor lasers
14
,
15
and a new F-P concept that can
be miniaturized to less than 1 cm
3
and chip-integrated without the need
for high-vacuum enclosure
8
,
16
–
18
. The frequency noise of two semicon
-
ductor lasers near 1,560 nm is reduced by 40 dB through self-injection
https://doi.org/10.1038/s41586-024-07058-z
Received: 21 July 2023
Accepted: 11 January 2024
Published online: xx xx xxxx
Open access
Check for updates
1
National Institute of Standards and Technology, Boulder, CO, USA.
2
Department of Physics, University of Colorado Boulder, Boulder, CO, USA.
3
T. J. Watson Laboratory of Applied Physics,
California Institute of Technology, Pasadena, CA, USA.
4
Department of Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA.
5
Department of
Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, USA.
6
Department of Applied Physics, Yale University, New Haven, CT, USA.
7
Jet Propulsion Laboratory,
California Institute of Technology, Pasadena, CA, USA.
8
Electrical Computer & Energy Engineering, University of Colorado Boulder, Boulder, CO, USA.
✉
e-mail:
igor.kudelin@colorado.edu
;
scott.diddams@colorado.edu
2
| Nature | www.nature.com
Article
locking (SIL) to high-Q (quality factor) Si
3
N
4
spiral resonators
6
,
7
. This
passive stabilization of the SIL laser enables further noise reduction, by
up to 60 dB, through Pound–Drever–Hall (PDH) locking to a miniature
F-P cavity, reaching the cavity’s thermal noise limit
6
,
19
.
In OFD, the optical phase noise of the reference is then reduced by
the square of the ratio of its frequency to that of the microwave output.
This is a powerful means for noise reduction by a factor as large as
(2
×1
0/
1×
10
)=
4×
10
14
10
28
or equivalently, 86 dB. However, significant
electrical power is required for generating a frequency comb spanning
approximately 200 THz with mode spacing of 10–20 GHz. Instead, we
use the simplified approach of 2P-OFD
4
,
5
,
20
,
21
, with comb bandwidth on
the order of 1 THz. This results in a lower division factor, but it also
significantly reduced size and power requirements. Such a trade-off
still allows us to reach an unprecedented microwave phase noise level
with integrated photonics because of the intrinsic low noise of the
optical references used.
In our system, the frequency division is implemented with another
injection-locked laser that generates a microcomb in a zero group
velocity dispersion (GVD) resonator, engineered by two coupled rings
in a Vernier configuration
9
. The microcomb operates without the need
for optical amplification, and approximately 30% of the input pump
power of 100 mW is efficiently transferred to the comb, which spans
nearly 10 nm. 2P-OFD is then implemented by heterodyning the two SIL
lasers with the closest comb teeth to produce two beat notes. These are
mixed to provide a servo control signal at an intermediate frequency
that is independent of the microcomb centre frequency. Upon phase
locking of the intermediate frequency, the noise of the microcomb is
dramatically reduced. Photodetection of the stabilized microcomb
output with a high-power and high-linearity modified unitravelling
carrier (MUTC) photodetector
22
provides a 20 GHz microwave signal
with phase noise of −135 dBc Hz
−1
at 10 kHz offset frequency. This level
of noise has not been achieved previously for a system that uses inte-
grated photonic components. We note that the critical photonic devices
used in our system can be further integrated to a single chip without
the need for fibre or semiconductor amplifiers or optical isolators,
providing ultrastable microwave generation in a compact form factor.
This advance is important for future applications of high-performance
microwave sources with compact size and low-power usage that will
operate beyond research laboratories.
Experiment and results
A technical illustration of the setup used for frequency comb stabi
-
lization and stable microwave generation is shown in Fig.
2
. Here, we
elaborate on the operation and characteristics of the key components,
concluding with a description of how they function together cohesively
to produce low-phase noise microwave signals.
Miniature F-P cavity
The phase and frequency stability of the generated microwave signal
is ultimately derived from that of the ultrastable optical reference.
The lowest-noise optical references are lasers locked to vacuum-gap
F-P cavities, where fractional frequency stability as low as 4 × 10
−17
has
been demonstrated with 212-mm-long cryogenic cavity systems
10
.
Instead, we use an integrable cavity design based on a compact, rigidly
held cylindrical F-P optical reference cavity that supports fractional
frequency stability at the 10
−14
level
8
. Ultralow expansion glass with 1 m
radius of curvature and an ultralow expansion glass spacer compose the
6.3-mm-long cavity with finesse of approximately 900,000 (Q ≈ 5 bil-
lion) and overall volume of less than 9 cm
3
. The cavity is thermal noise
limited for offset frequencies ranging from 1 Hz to 10 kHz. Moreover,
the relative phase noise between two reference lasers locked to the
same cavity takes advantage of large common-mode rejection (CMR),
reaching 40 dB rejection for cavity modes spaced by 1 THz (ref.
18
).
When combined with 2P-OFD, the cavity noise is expected to be reduced
by approximately 80 dB when projected onto the microwave carrier.
Self-injection-locked lasers
To achieve high-stability performance, it is crucial to use narrow-
linewidth and frequency-stable lasers. This is because electrical noise
from the individual laser locking circuits does not experience CMR,
and this noise is reduced only by the 2P-OFD. To address this issue and
reach the thermal noise floor of the F-P cavity, we use SIL lasers that
are both integrable and have noise performance equivalent to much
larger laboratory fibre lasers
6
,
7
,
14
. With reference to Fig.
2
, two commer-
cial semiconductor distributed feedbacks (DFBs) are prestabilized
by SIL to a high-Q Si
3
N
4
spiral resonator
7
. When the forward and back
-
ward fields between the DFB lasers and the Si
3
N
4
resonators are in
phase, resonant backscattered light is fed back to the DFB, anchoring
each laser wavelength to the corresponding Si
3
N
4
resonance and sig
-
nificantly suppressing its frequency noise. This passive prestabiliza
-
tion of the DFB lasers is crucial to reach the thermal noise limit of the
F-P cavity and reduce the high-frequency noise. The length and Q of
the integrated resonator determine the ultimate phase noise of the
Stable reference
a
b
c
F-P cavity
Microresonator
modes
Cavity modes
Microcomb
Phase-locked
loop
MUTC
Detection
Microwave signal
SIL laser
Q
CW1
Q
CW2
Q
0
nm
g
b2
g
rep
g
b1
g
IF
=
g
b1
+
g
b2
I
g
rep
=
Q
CW2
–
Q
CW1
–
g
IF
m
+
n
Optical frequency division
Fig. 1 | Concept of 2P-OFD for low-noise microwave generation.
a
, Two
semiconductor lasers are injection locked to chip-based spiral resonators. The
optical modes of the spiral resonators are aligned, using temperature control,
to the modes of the high-finesse F-P cavity for PDH locking.
b
, A microcomb is
generated in a coupled dual-ring resonator and is heterodyned with the two
stabilized lasers. The beat notes are mixed to produce an intermediate
f r e q u e n c y,
f
IF
, that is phase-locked by feedback to the current supply of the
microcomb seed laser.
c
, An MUTC photodetector chip is used to convert the
microcomb’s optical output to a 20 GHz microwave signal.
Nature | www.nature.com |
3
SIL laser
23
, and here, we use a spiral with a length of 1.41 m that is fab
-
ricated on approximately 1 cm
2
of silicon. The intrinsic and loaded Q
factors of the two spiral resonators are 164 and 126 million
7
. The outputs
of the SIL lasers are amplified using commercial erbium-doped fibre
amplifiers (EDFAs) to approximately 30 mW and then further stabilized
via PDH locking to the miniature F-P cavity. In this setup, the primary
actuator for PDH stabilization is an acousto-optic modulator; however,
the PDH error signal is also fed back to the electro-optical modulator
(EOM) to further increase the bandwidth and noise reduction of the
PDH servo
24
. The in-loop phase noise of the PDH locking of SIL lasers
is presented in Methods.
Microcomb
Robust and low-noise optical frequency comb generation with
10–20 GHz repetition rate and broad optical coverage is challenging.
Here, we use an Si
3
N
4
microresonator fabricated at a complementary
metal-oxide semiconductor (CMOS) foundry to generate mode-locked
microcombs
14
. To produce dark soliton microcombs with higher band
-
width, we use a dual coupled-ring resonator with free-spectral range
(FSR) of 20 GHz (ref.
9
), where the zero GVD wavelength is tuned to
approximately 1,560 nm using integrated heaters
25
. In addition, such
microcomb states have high pump-to-comb conversion efficiency,
benefiting microwave generation in a low-SWaP system. To generate the
comb, a commercial semiconductor DFB laser without optical amplifi
-
cation is self-injection-locked to the dual coupled-ring resonator, which
narrows the linewidth of the pump laser and generates a reasonably
stable 20 GHz comb
14
,
26
,
27
. Following the coupled rings, a notch filter
is used to suppress the central (seed) comb line to avoid saturation in
an EDFA, which amplifies the frequency comb up to 60 mW (Fig.
2
).
Note that the use of a drop port on the coupled-ring resonator can
replace the notch filter. A typical comb spectrum after the EDFA is
shown in Fig.
3b
.
Microcomb stabilization and microwave generation
As outlined above, in this work we use two-point locking to realize
OFD for phase noise reduction. With appropriate fibre optic couplers
and filters, we design a receiver system to separate heterodyne beat
notes and 20 GHz microwave generation. The two beat notes between
the microcomb and each continuous wave (CW) laser are given by
f
b1
= (
ν
0
−
n
f
rep
) −
ν
CW1
and
f
b2
=
ν
CW2
− (
ν
0
+
m
f
rep
) (Fig.
1
). Here, the
comb modes are indexed with signed integers from the central (seed)
frequency
ν
0
. These beats are filtered, amplified and mixed together to
produce the intermediate frequency (
f
IF
), which is then phase-locked to
a stable microwave reference via feedback to the current of the micro
-
comb seed laser
9
. The stabilization of
f
IF
is the final step to generate a
low-noise microwave via 2P-OFD:
f
IF
=
f
b1
+
f
b2
=
ν
CW2
−
ν
CW1
− (
n
+
m
)
f
rep
,
where
n
+
m
is the value of the OFD (32 in our case) that amounts to 30 dB
of noise reduction. Note that two-point locking does not depend on
the noise of the microcomb central frequency
ν
0
. Thus, the instability
of the microcomb repetition rate can be represented as
8 mm
*
20 GHz
output
MUTC
DFB
laser
Si
3
N
4
microresonator
Mini F-P
cavity
PD
ISO
ISO
AOM
PM
AOM
PM
PD
Notch
lter
Current
supply
Servo
PD
Si
3
N
4
microresonator
Mini F-P cavity
8 mm
~1.5 cm
4 mm
1 mm
Si
3
N
4
coupled rings
MUTC
Q
CW1
EDFA
Q
CW2
EDFA
Si
3
N
4
microresonator
DFB
laser
DFB
laser
Q
0
g
IF
=
g
b1
+
g
b2
g
b1
g
b2
g
rep
EDFA
Si
3
N
4
coupled
rings
Fig. 2 | Experimental setup.
Two DFB lasers at 1, 557.3 and 1, 562.5 nm are
self-injection-locked to Si
3
N
4
spiral resonators, amplified and locked to the
same miniature F-P cavity. A 6 nm broad-frequency comb with an approximately
20 GHz repetition rate is generated in a coupled-ring resonator. The microcomb
is seeded by an integrated DFB laser, which is self-injection-locked to the
coupled-ring microresonator. The frequency comb passes through a notch
filter to suppress the central line and is then amplified to 60 mW total optical
power. The frequency comb is split to beat with each of the PDH-locked SIL
continuous wave references. Two beat notes are amplified, filtered and then
mixed together to produce
f
IF
, which is phase-locked to a reference frequency.
The feedback for microcomb stabilization is provided to the current supply of
the microcomb seed laser. Lastly, part of the generated microcomb is detected
in an MUTC detector to extract the low-noise 20 GHz signal. Photographs of the
key photonic components used in low-noise microwave generation are in the
lower panels. Scale bars (from left to right), 8 mm; approximately 1.5 cm; 4 mm;
1 mm. ISO, optical isolator; PM, phase modulator; PD, photodetector.
4
| Nature | www.nature.com
Article
δf
δν
νδ
f
nm
=
(−
)+
(+
)
.
re
p
2
CW
2C
W1
2
IF
2
2
Although the phase noise of
f
IF
,
ν
CW1
and
ν
CW2
is reduced by 2P-OFD,
their servo control and residual noise can be limiting factors in the
achievable microwave phase noise (Methods).
The stabilized microcomb output is directed to an MUTC photodiode,
which provides exceptional linearity and large microwave powers
28
,
29
.
We tune the bias voltage of the MUTC operation for approximately
40 dB rejection of amplitude-to-phase noise conversion while gen
-
erating a 20 GHz power of −10 dBm at 5 mA of average photocurrent.
The 20 GHz microwave signal is filtered and amplified to +3 dBm, and
it is sent to a measurement system, with results presented in Fig.
3a
.
Here, we have scaled the measured 20 GHz phase noise to 10 GHz by
subtracting 6 dB. This yields −102 dBc Hz
−1
at 100 Hz, which decreases
to −141 dBc Hz
−1
at 10 kHz. We also compare with a 10 GHz carrier that
we generate from 20 GHz with a regenerative divide-by-two circuit.
Compared with the free-running microcomb generation, we achieved
more than 50 dB phase noise improvement for offset frequencies below
10 kHz. Additional details on the phase noise measurement and divider
are in Methods.
Discussion and further integration
Figure
4
places the level of phase noise we achieve in context with other
photonic approaches, including recent works based on microcombs
and mode-locked laser frequency combs. The comparison is classified
by level of photonic integration of the microcomb source and pumping/
reference lasers, as applicable. It is also noted that some of the micro
-
comb systems require the assistance of a fibre-based frequency comb
(Fig.
4ix,x
)
30
,
31
. The phase noise performance of other systems, which
could be chip integrated (Fig.
4ii,iii
)
14
,
32
, is more than 30 dB greater than
the results we present, with the exception of the recent work by Sun
et al. (Fig.
4vi
)
33
. Other notable works on low-noise microwave genera
-
tion in low-SWaP systems, which are not shown in Fig.
4
, include ‘quite
point’ operation
31
,
34
–
36
, single-laser OFD
37
and high-end commercial
products
38
–
40
.
To the best of our knowledge, this work provides the best phase
noise performance in the frequency range of 200 Hz to 40 kHz for
microcomb-based systems. Importantly, it does so with integrated
photonic components that can all be further combined onto a sin
-
gle chip with total volume of the photonic components of approxi
-
mately 1 cm
3
. A concept of such a fully integrated system is shown in
Fig.
5a
and would consist of heterogeneously integrated lasers near
>50 dB
–70
–80
–90
–100
–110
–120
–130
–140
–150
Phase noise (dBc Hz
–1
)
10
2
10
3
10
4
10
5
10
6
Frequency (Hz)
Free-running scaled to 10 GHz
20 GHz locked scaled to 10 GHz
20 GHz locked with divide by 2
10
0
–10
–20
–30
–40
–50
Power (dBm)
1,555
1,556
1,557
1,558
1,559
1,560
1,561
1,562
1,563
1,564
Wavelength (nm)
0
–20
–40
–60
Power (dB)
–0.2
–0.1
00
.1
0.2
Offset from carrier (MHz)
Power (dB)
0
–25
–50
–75
–0.2
–0.1
00
.1
0.
2
Offset from carrier (MHz)
a
b
cd
5.17 nm , 637 GHz
Fig. 3 | Microcomb characterization.
a
, Single side-band phase noise scaled to
10 GHz of free-running 20 GHz microcomb (blue), locked 20 GHz microwave
(red) and locked 20 GHz microwave after regenerative frequency division by
two (green).
b
, Optical spectrum of microcomb (grey) and SIL lasers (green and
turquoise).
c
,
d
, Radio frequency spectra of 20 GHz signal free running
(resolution bandwidth (RBW) 100 Hz;
c
) and locked (RBW 1 Hz;
d
).
–160
–150
–140
–130
–120
–110
–100
This work
SSB phase noise at 10 kHz (dBc Hz
–
1)
Volume
–170
Stand-alone microcomb
OFD-based microcomb
Integrated
Fibre comb-assisted microcomb
Fibre optic/mode
lock laser-based OFD
Typical
RF synthesizers
~10
4
cm
3
~10 cm
3
vi
viii
vii
ix
x
v
iv
iii
ii
i
Bulk element
Fig. 4 | Phase noise comparison of microwave generation based on
microcombs.
The platforms are all scaled to 10 GHz carrier and categorized
based on the integration capability of the microcomb generator and the
reference laser source, excluding the interconnecting optical/electrical parts.
Filled (blank) squares are based on the OFD (stand-alone microcomb) approach:
(i) 22 GHz silica microcomb
50
; (ii) 5 GHz Si
3
N
4
microcomb
14
; (iii) 10.8 GHz Si
3
N
4
microcomb
32
; (iv) 22 GHz microcomb
51
; (v) MgF
2
microcomb
52
; (vi) 100 GHz
Si
3
N
4
microcomb
33
; (vii) 22 GHz fibre-stabilized SiO
2
microcomb
21
; (viii) MgF
2
microcomb
53
; (ix) 14 GHz MgF
2
microcomb pumped by an ultrastable laser
30
;
and (x) 14 GHz microcomb-based transfer oscillator
31
. SSB, Single side band.
Nature | www.nature.com |
5
1,560 nm (ref.
6
), spiral resonators
7
for SIL, a coupled-ring microcomb
resonator
9
, photodetectors
22
and a microfabricated F-P cavity that
does not require high vacuum
16
,
18
.
Previous work already laid out the steps for heterogeneous integra
-
tion of lasers and Si
3
N
4
resonators. For example, InP lasers and Si
3
N
4
resonators have been integrated on the same chip with coupling
between the optical gain and low-loss waveguide layers facilitated by
adiabatic tapers, with resonator waveguide losses down to 0.5 dB m
−1
with a second deeply buried Si
3
N
4
waveguide layer
15
,
41
. This same hetero
-
geneous integration with ultrahigh-Q resonators promises isolator-free
operation
41
. A similar strategy has been used for laser integration with
780-nm-thick Si
3
N
4
anomalous dispersion microcombs on the same
chip
42
, which can be applied to the 100-nm-thick Si
3
N
4
zero GVD micro
-
combs used in this work. Furthermore, laser integration with modula
-
tors and detectors has also been previously demonstrated
43
and can be
utilized for full integration of all the optical components comprising
the PDH locking system
44
.
The integration of the active and passive components on a single
platform greatly reduces loss (between fibre and chip) and removes
the need for the optical amplifiers we have used in the present work.
In such a case, a few tens of milliwatts of optical power is required to
pump the resonator such that a comb with a few milliwatts of optical
power and several microwatts per mode is realistic. Additionally, for
the SIL lasers, only several milliwatts of DFB optical power is required to
provide a hundred microwatts of optical power to heterodyne with the
comb and achieve the signal-to-noise ratio (SNR) necessary to match
the performance presented in this work. For recent integrated lasers,
these powers are realistic
15
. Additional considerations on required
optical power are discussed in Methods.
Integration of the F-P cavity has been an outstanding challenge,
but recent developments in microfabricated mirrors
16
and compact
thermal-noise-limited F-P designs
17
provide new integration opportu
-
nities. Critically, it has been shown that 2P-OFD does not require F-P
operation in high vacuum because of CMR
18
, significantly simplifying
future integration. Figure
5
shows a 1 cm
3
cavity with fabricated micro
-
mirrors and details on an integration strategy with the SIL lasers and
microcomb. A planar waveguide feeds an inverse-designed polariza
-
tion splitting grating embedded in an interferometer, which serves to
shape the beam for coupling light to the cavity while also providing the
cavity-reflected PDH locking signal and laser isolation
45
. Preliminary
measurements described in Methods demonstrate the feasibility of
this approach. The F-P cavity and a gradient-index (GRIN) lens can be
bonded on top of the polarization splitting grating in a hybrid flip-chip
fashion for a single-chip, cavity-integrated, low-noise microwave gen
-
erator unit.
In the integration scheme, the acousto-optic modulators (AOMs)
can be replaced with a combination of slow feedback to the integrated
heaters or piezoelectric components
46
in the spirals and fast feedback
to DFB current and EOMs
24
. The thermal tuning can reach a bandwidth
of a few kilohertz
41
,
47
, whereas the fast feedback with a bandwidth of
several megahertz could be provided by the EOM or current modula-
tion
43
,
44
. We estimate that this combination can provide 40 dB feedback
gain at 10 kHz offset frequency to match the phase noise performance
of the presented work. To further reduce the size of the entire system,
the modulation frequencies for the PDH locking, as well as for phase
locking of the intermediate frequency, could be synthesized by using
a direct digital synthesizer, clocked by the microwave derived from
the microcomb itself
48
,
49
.
In summary, we have demonstrated an integrated photonic approach
to OFD that produces 20 GHz microwave signals with phase noise of
−135 dBc Hz
−1
at 10 kHz offset, a value typical of much larger existing
commercial systems. This is accomplished with a unique combination
of low-noise integrated lasers, an efficient dark soliton frequency comb
and new advances in a miniature F-P optical cavity. Significantly, our
approach provides a route to full integration on a single chip with vol-
ume of the photonic components on the order of 1 cm
3
. This advance
in integrated photonic low-noise microwave generation holds promise
for compact, portable and low-cost microwave synthesis for a wide
variety of demanding applications in navigation, communications
and precise timing.
Online content
Any methods, additional references, Nature Portfolio reporting summa
-
ries, source data, extended data, supplementary information, acknowl
-
edgements, peer review information; details of author contributions
and competing interests; and statements of data and code availability
are available at
https://doi.org/10.1038/s41586-024-07058-z
.
DFB lasers
Heaters
EOMs
~1 cm
20 GHz output
EOMs
Grating coupler
F-P cavity
Spiral resonator
Spiral resonator
MUTC
Dual-ring
resonator
Fig. 5 | Schematic design of a photonic microwave oscillator on a single chip.
The integrated system uses the same key photonic elements used in this work.
Two spiral resonator SIL lasers are PDH locked to the same micro-F-P cavity with
two EOMs in series for each SIL laser—the first for fast phase correction and the
second for PDH side bands. The right side of the schematic shows the F-P cavity
interface, where the two SIL laser paths are fed through an interferometer with
an embedded polarization splitting grating. This serves as a ref lection
cancellation circuit while also shaping the planar waveguide mode to match the
F-P mode
45
. The ref lection from the F-P cavity is then detected by the right-most
detector. The inset shows a photo of the miniature F-P cavity consisting of
microfabricated mirrors
16
, with overall volume of approximately 1 cm
3
. Scale
bar, approximately 1 cm. Illustration reproduced with permission from B. Long.
6
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Methods
Characterization of the noise contributions to the microwave
noise
Extended Data Fig. 1 shows the phase noise of the various compo
-
nents that contribute to the generated 20 GHz signal. This includes
the in-loop phase noise and SNR of each continuous wave laser and
the intermediate frequency, the SNR of the 20 GHz carrier and inten-
sity noise projected onto the microwave phase because of finite
amplitude-to-phase rejection. The in-loop phase noise of continuous
wave lasers was estimated as described in ref.
54
. The SNR of the con-
tinuous wave lasers is estimated in a similar way but when the lasers
are unlocked and detuned from the F-P cavity resonance. The in-loop
phase noise of the intermediate frequency was directly measured by
using a commercial phase noise measurement system. Note that the
aforementioned measured noise terms, excluding amplitude-to-phase
conversion, were scaled down by 30 dB to account for their reduc
-
tion because of OFD. The amplitude-to-phase conversion was deter
-
mined from the measured relative intensity noise of the microcomb on
the MUTC photodetector after scaling down by the amplitude-to-phase
rejection (40 dB). The rejection value was measured by modulating
the microcomb optical power and comparing the strength of ampli
-
tude modulation tone with the resulting phase modulation on the
20 GHz carrier.
At frequencies below 1 kHz, the phase noise of the 20 GHz signal is lim
-
ited by the electronic noise of the PDH locks, which could be improved
by increasing the 2P-OFD phase noise reduction (that is, by using a
microcomb with broader bandwidth). At frequencies above several
tens of kilohertz, the phase noise increases because of the limited gain
and bandwidth of the microcomb feedback loop. The phase noise of
the 20 GHz signal at frequencies above 1 MHz follows the phase noise
of the free-running signal, which can be found in ref.
9
. High-frequency
noise could be decreased by using a more stable free-running micro
-
comb state or by improving the feedback bandwidth. As can be seen,
in the range between 1 and 40 kHz, the listed noise contributions do
not affect the microwave generation, which decreases as 1/
f
. A possible
source of noise in this region is microcomb noise that is uncorrelated
between modes separated by approximately 640 GHz. Another possible
limitation that restricts the noise floor is the limited servo gain, which
already provides more than 50 dB reduction in that region. Mitigating
these constraints would allow for a further decrease of the noise in that
region by up to 10 dB.
Electronics for microcomb stabilization and phase noise
measurement
Extended Data Fig. 2a shows the electronics used for microcomb sta-
bilization. Both beat notes between continuous wave lasers and the
microcomb teeth are filtered, amplified and mixed together to produce
the intermediate frequency (
f
IF
) at 2.6 GHz. The IF frequency is further
amplified and mixed with a reference oscillator to produce an error
signal for microcomb stabilization. The error signal is fed to a servo,
which provides feedback to the current supply of the seed laser. Note
that the noise of the reference oscillator in this servo is divided down
by the 2P-OFD, and in a future implementation, it could be obtained
from the division of the 20 GHz signal itself.
Extended Data Fig. 2b illustrates the experimental setup for measur-
ing phase noise of the 20 GHz signal. To measure the phase noise of the
microcomb, we used the ultrastable microwave from a self-referenced
Er:fibre frequency comb
2
as a reference oscillator. This Er:fibre comb
was used only for the measurement purpose. The microcomb optical
signal and the reference Er:fibre comb are detected by using two MUTC
detectors. Then, the 20 GHz signal under test and the reference 20 GHz
are filtered, amplified and split. The reference microwave signal is
further amplified to saturate the mixers. Each arm of the microwave
signal from the microcomb is mixed with the reference microwave to
produce two signals at 47 MHz. Two arms are used for cross correlation
to remove the additional noise from the microwave amplifiers in the
reference branch. The cross correlation was realized with a commercial
phase noise analyzer.
The phase noise of the reference 20 GHz is shown in Extended Data
Fig. 2c. To measure the phase noise of the reference signal, we cross cor
-
related it with two microwave oscillators for 3 h. The approximated
measurement floor, shown in Extended Data Fig. 2c, represents the
phase noise of the microwave oscillators and the cross correlation gain
(30 dB) because of the finite number of averages.
Regenerative divide by two
Extended Data Fig. 3a shows the scheme of the regenerative divide
by two, which consists of a double-balanced mixer, 10 GHz amplifier,
power splitter and phase shifter
55
. The phase shifter is used to control
the phase delay inside the divider. The input 20 GHz is amplified up
to approximately +13 dBm to saturate the local oscillator port of the
double-balanced mixer. The IF port with 10 GHz signal is then ampli
-
fied and split to provide the output signal with power of approximately
+10 dBm. The output 10 GHz is measured using the same setup as shown
in Extended Data Fig. 2b, whereas the reference signal at 10 GHz is pro
-
vided from the same fibre frequency comb.
Extended Data Fig. 3b provides the schematic of the setup for measur
-
ing the phase noise of the divider. The input signal is split and fed to two
separate dividers. The outputs from the dividers are cross correlated
with the phase noise analyser. Because of the cross correlation, the cor
-
related noise between both signals (that of the input signal) is averaged
out, providing the phase noise of the divider itself. The phase noise of
the divider at carrier input frequencies 16 and 18 GHz is presented in
Extended Data Fig. 3c.
Optical power requirements for the integrated system
Here, we consider the required optical power to achieve the perfor
-
mance presented in the paper. In the experimental demonstration
described in the main text, the purpose of the optical amplifiers was to
compensate the coupling losses between the SIL lasers and the chips
and between the chips and the lens fibres. This ensured that all photo
-
detected signals had the power needed to increase the SNR, limited by
the thermal noise, to the required level. Extended Data Fig. 4a shows the
calculated achievable SNR as a function of microcomb optical power
when compared with the noise floor that consists of thermal and shot
noise. Here, we assume detection with the MUTC having quantum
efficiency of 0.5. To reach the same performance that we demonstrate
in this present work, but without optical amplification, would require
only a few hundred microwatts of comb optical power on the 20 GHz
photodetector. Extended Data Fig. 4b shows the calculated SNR of the
beat notes against the optical power of the SIL laser for three different
comb tooth powers. As can be seen, to reach the performance presented
in this work, it would be sufficient to combine tens of microwatts of
SIL laser power with a few microwatts of comb tooth power. In our
work, the heterodyne detection of the beat note with the SIL lasers
used comb teeth with power of approximately 50 μW, whereas the total
comb power before optical couplers was 60 mW. Thus, assuming that
the losses after the microcomb generation are similar to this work, to
provide comb teeth power of a few microwatts with a similar spectrum
shown in Fig.
2
, only several milliwatts of the total microcomb optical
power would be required. To provide tens of microwatts from the SIL
reference laser for heterodyning, the optical power on the order of a few
hundred microwatts from the spiral resonator is required. This implies
only a few milliwatts of power directly from the DFB laser.
Nonetheless, the single-chip integration would mitigate the coupling
losses and increase the system efficiency. Additionally, removing AOMs
would improve the power of the reference SIL lasers by approximately
3–5 dB, which is the insertion loss of the AOMs we used. In conclusion,
these numbers are realistic to achieve with present integrated lasers
15
.
Article
Cavity with microfabricated mirrors
In this work, we propose to use a cavity with microfabricated mirrors
16
,
which can be realized in a cube with overall volume below 1 cm
3
and
does not require operation in vacuum (inset in Fig.
5
). Extended Data
Fig. 5a shows the ring-down measurement of such a cavity at 1,550 nm.
The cavity has 60 kHz linewidth and provides finesse of 428,000 and
Q ≈ 2 billion. This measurement indicates that such a compact cavity has
the required linewidth to provide the necessary SNR in the PDH locking.
Extended Data Fig. 5b schematically shows the cavity integration with
the chip. The light from the waveguide is redirected to the integrated
grating coupler. The output light from the grating is collected with
a GRIN lens that optimally matches the output of the grating to the
cavity mode. To avoid the back reflection from the cavity and reroute
the reflected signal to another port for PDH detection, we design the
on-chip circuits that are shown in Extended Data Fig. 5c and described in
more details in ref.
45
. The input light is split 50/50 and then recombined
at the on-chip polarization splitting grating coupler
56
into a circularly
polarized beam that is directed into free space. The reflected light
from the cavity will switch the handedness and be collected by the
polarization splitting grating coupler. By interfering two polarizations
of reflected light in a 50/50 on-chip beam splitter, the back reflection
is cancelled, and the signal rerouting is achieved.
To characterize the performance of this system, we use an SMF28
fibre to collect the output light from the polarization splitting grating
coupler. The other end of fibre is connected to the GRIN lens, which
then transfers the light into the cavity. The system was used as a proof
of principle to measure the transmission and back reflection of the
grating-GRIN-cavity system; those results are shown in Extended Data
Fig. 5d. The insertion loss of the system is approximately −7 dB, whereas
back reflections toward the laser source are reduced by −17 dB. Note
that this system includes additional losses because of the inserted
fibre, and the efficiency can be further improved by avoiding that step.
Also, the back-reflection suppression ratio can be further improved
by implementing an on-chip tunable coupler to achieve a more ideal
50/50 splitting ratio. These results provide confidence that the micro
-
fabricated cavity can be successfully integrated onto a planar chip.
Data availability
All data for the figures in this manuscript are available at
https://doi.
org/10.6084/m9.figshare.24243511
.
54.
Schmid, F., Weitenberg, J., Hänsch, T. W., Udem, T. & Ozawa, A. Simple phase noise
measurement scheme for cavity-stabilized laser systems.
Opt. Lett.
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, 2709–2712
(2019).
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Hati, A. et al. Ultra-low-noise regenerative frequency divider.
IEEE Trans. Ultrasonics
Ferroelectrics Freq. Control
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, 2596–2598 (2012).
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Zaoui, W. S., Kunze, A., Vogel, W. & Berroth, M. CMOS-compatible polarization splitting
grating couplers with a backside metal mirror.
IEEE Photon. Tech. Lett.
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Acknowledgements
We thank B. Long for the illustration in Fig.
5
and K. Chang and
N. Hoghooghi for comments on the manuscript. Commercial equipment and trade names are
identified for scientific clarity only and do not represent an endorsement by NIST. The research
reported here performed by W.Z., V.I. and A.M. was carried out at the Jet Propulsion Laboratory
at the California Institute of Technology under a contract with the National Aeronautics and
Space Administration. This research was supported by the DARPA GRYPHON Program
(grant HR0011-22-2-0009), the National Aeronautics and Space Administration (grant
80NM0018D0004) and NIST.
Author contributions
P.T.R., J.E.B., K.J.V., A.M., F.Q. and S.A.D. conceived the experiment and
supervised the project. I.K., W.G. and S.A.D. wrote the paper with input from all authors. I.K. and
W.G. together with Q.-X.J. and J.G. built the experiment and performed the optical frequency
division experiment. L.W. prepared the distributed feedback laser butterfly packages for the
experiment. Q.-X.J., J.G., W.J., L.W., C.X. and L.C. prepared the microcomb and spiral resonators
for the experiment. M.L.K. and F.Q. built the Fabry–Pérot cavity. D.L., T.N., C.A.M., Y. Liu and F.Q.
provided the optically derived microwave reference and aided in the microwave phase noise
measurement system. P.S., S. Hanifi and S.M.B. provided the regenerative divide-by-two circuit.
H.C., N.J., S. Halladay, Z.D., Y. Luo, O.M., F.Q. and P.T.R. contributed to the cavity integration
scheme. W.Z., V.I. and A.M., contributed to phase noise limitation analysis and system
integration. J.B. and J.C.C. provided modified unitravelling carrier detectors. All authors
contributed to the system design and discussion of the results.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information
The online version contains supplementary material available at
https://doi.org/10.1038/s41586-024-07058-z
.
Correspondence and requests for materials
should be addressed to Igor Kudelin or
Scott A. Diddams.
Peer review information
Nature
thanks the anonymous reviewers for their contribution to the
peer review of this work. Peer reviewer reports are available.
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.