Research Article
Vol. 11, No. 11 / November 2024 /
Optica
1583
Photonic millimeter-wave generation beyond the
cavity thermal limit
William Groman,
1
,
2
,
3
,
*
Igor Kudelin,
1
,
2
,
3
Alexander Lind,
1
,
3
Dahyeon Lee,
2
,
3
Takuma Nakamura,
3
Yifan Liu,
2
,
3
Megan L. Kelleher,
2
,
3
Charles A. McLemore,
2
,
3
Joel Guo,
4
Lue Wu,
5
Warren Jin,
4
Kerry J. Vahala,
5
John E. Bowers,
4
Franklyn Quinlan,
1
,
3
AND
Scott A. Diddams
1
,
2
,
3
1
Electrical Computer & Energy Engineering, University of Colorado, Boulder, Boulder, Colorado 80309, USA
2
Department of Physics, University of Colorado, Boulder, 440 UCB, Boulder, Colorado 80309, USA
3
National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
4
Department of Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, USA
5
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
*william.groman@colorado.edu
Received 15 July 2024; revised 3 October 2024; accepted 4 October 2024; published 14 November 2024
Next-generation communications, radar, and navigation systems will extend and exploit the higher bandwidth of the
millimeter-wave domain for increased communication data rates as well as radar with higher sensitivity and increased
spatial resolution. However, realizing these advantages will require the generation of millimeter-wave signals with low
phase noise in simple and compact form-factors. Photonic integration addresses this challenge and provides a path
toward simplified and portable, low-noise mm-wave generation. We leverage these advances by heterodyning two silicon
photonic chip lasers, phase-locked to different axial modes of a miniature Fabry–Perot (F-P) cavity to demonstrate a
simple framework for generating low-noise millimeter-waves. By reducing technical noise, we achieve common-mode
rejection of the thermally driven Brownian noise such that the millimeter-wave phase noise surpasses that of the ther-
mal limit of a single laser locked to the F-P cavity. This leads to a 118.1 GHz millimeter-wave signal with phase noise of
−
118 dBc
/
Hz at 10 kHz offset, decreasing to
−
120 dBc
/
Hz at 30 kHz offset. We achieve this with technologies that can
be integrated into a platform less than
≈
10 mL. Our work overcomes fundamental thermal-mechanical noise limits
intrinsic to integrated photonics, while illustrating advantages of the same for providing low-size, -weight, and -power
(SWaP) mm-waves that will be enabling for multiple applications in communications and sensing.
© 2024 Optica
Publishing Group under the terms of the Optica Open Access Publishing Agreement
https://doi.org/10.1364/OPTICA.536549
1. INTRODUCTION
Inherent in the higher frequency of millimeter-wave carriers (mm-
wave,
≈
30
→
300 GHz) is the capability of higher modulation
bandwidth and faster data transfer rates [1,2], finer radar and
sensing spatial resolution [3,4], antenna miniaturization [3], and
the potential for effective atmospheric transmission. [5]. The
impact of mm-waves is already evident in cutting-edge telecom-
munications, with 5G utilizing carriers in both the microwave and
low mm-wave range (
/
50 GHz), and 6G technology pushing
carrier frequencies beyond 90 GHz [6]. Furthermore, mm-wave
technologies have already shown promise for safe and non-invasive
biomedical and security sensing applications [7,8], and are widely
used as radio astronomy references [9].
In the microwave range, rack-mount-volume synthesizers
dominate the application space. These provide wide tunability, but
with close-to-carrier phase noise that, in the best case, is given by a
frequency-multiplied quartz reference or other dielectric oscillator.
Such signal sources are commonly extended to the mm-wave via
carrier multiplication by
N
, but that comes with additional degra-
dation in phase noise power spectral density by at least 20 log
(
N
)
[10]. As a result, commercial mm-wave synthesizers at 100 GHz
are typically limited in phase noise performance in the range of
−
100 dBc
/
Hz at 10 kHz offset and often fall short in meeting the
demands as local oscillators (LOs) in the aforementioned radar and
telecommunication applications. On the other hand, laboratory
research synthesizers provide remarkably low noise at the cost of
increasing complexity and larger volume [11].
Within this context, the field of mm-wave photonic synthesis
with narrow-linewidth lasers provides a compelling alternative
to electronic approaches. Most simply, the interference of two
continuous wave (CW) lasers can be photomixed (photodetected)
to produce a mm-wave signal at the difference frequency of the
lasers. This concept was first demonstrated just a few years after the
invention of the laser, but progress has accelerated over the past two
decades with multiple techniques involving lasers, electro-optics,
and frequency combs to generate and control the relative frequency
difference between the CW lasers [12–20].
2334-2536/24/111583-05 Journal © 2024 Optica Publishing Group
Research Article
Vol. 11, No. 11 / November 2024 /
Optica
1584
Even greater opportunities for photonic mm-waves are offered
by the confluence of recent advances in chip-integrated low-noise
lasers and frequency combs and the means to frequency-stabilize
these light sources with compact, high-finesse, and integrable
high-Q optical cavities. Importantly, lasers can now be hetero-
geneously integrated on a CMOS-compatible platform together
with extremely low-loss Si
4
N
3
ring resonators for self-injection
locking (SIL) operation [21,22]. This leads to laser frequency
noise that is typically associated with narrow-linewidth fiber lasers,
but with a smaller footprint [23]. In addition, miniaturization
and integration of centimeter-sized optical cavities with finesse
approaching 10
6
[24,25] transforms the realization of hertz-
linewidth lasers from large laboratory setups to the chip-scale,
and in some cases even forgoing the need for vacuum enclosures
[25]. Recent combinations of such integrated photonic hardware
have further utilized the powerful approach of optical frequency
division (OFD) for low-noise microwave and mm-wave generation
[26,27].
In this work, we show that the benefits of OFD are not required
to further advance the phase noise of mm-wave generation at
100 GHz and above. Instead we exploit the high degree of thermal
noise correlation and common-mode noise rejection between the
axial modes of a Fabry–Perot (F-P) to strongly reject this noise in
mm-wave generation. A cavity Q-factor approaching 10
10
and
linewidth near 20 kHz allow us to tightly lock the frequencies of
two lasers to cavity modes with residual noise that is well below
the room-temperature cavity thermal noise. Thus, the correlated
thermal noise of the cavity close-to-carrier that is imprinted on
each laser is subtracted in the mm-wave heterodyne beat.
We implement this concept with two SIL lasers that are
frequency-locked to modes of a miniature high-Q Fabry–
Perot cavity with free spectral range, FSR
=
23.6 GHz. For
modes separated by 5
×
FSR
=
118 GHz, the phase noise of the
heterodyne beat is
−
118 dBc
/
Hz at 10 kHz offset, decreasing to
−
120 dBc
/
Hz at 30 kHz. Importantly, our approach uses the same
components that have been shown to be compatible with chip-
scale integration, while offering phase noise levels that match those
achieved with more complicated integrated OFD approaches. And
at 10 kHz offset our results are close to the noise levels achieved in
the very best photonic mm-wave laboratory experiments.
Our straightforward approach to mm-wave generation effec-
tively removes the fundamental limitations imposed by cavity
thermal noise. As such, we anticipate that further improvements
in phase noise performance will be allowed to proceed at the more
rapid pace of technical innovations in low-noise chip-integrated
lasers and frequency control techniques.
2. CONCEPT AND EXPERIMENT
Figure 1(a) shows a simplified schematic of the experiment.
Starting from the left, two distributed-feedback (DFB) lasers (
ν
1
and
ν
2
) are individually coupled and self-injection locked to sepa-
rate high-Q (Q
'
10
8
) Si
3
N
4
microresonators, with free spectral
ranges (FSRs) of about 135 MHz. The self-injection locking is
controlled by fine-tuning the facet distance, and thereby the phase,
of the DFBs relative to their respective microresonator chips, and
results in a phase noise suppression of the free-running DFB signal
by up to 50 dB [28]. The SIL laser output is then fiber-coupled out
of the chip for use.
This initial self-injection locking suppresses the close-to-
carrier noise and allows us to use the Pound–Drever–Hall (PDH)
technique [29] to subsequently lock each laser’s frequency to an
ultra-stable, temperature- and vacuum-controlled, miniature F-P
cavity. In this case, the laser frequency inherits the stability of the
cavity, but with frequency noise fundamentally limited by ther-
mally driven stochastic fluctuations in the cavity length [30]. Here,
the cavity we used is exhibited and referred to in [31] as the “all-
ULE cavity”. We lock both lasers to separate F-P cavity modes such
that the mm-wave carrier frequency is
f
μ
=
n
×
FSR
=
ν
1
−
ν
2
,
as portrayed in Fig. 1(c). Importantly, subtraction of these two
PDH-locked signals, as occurs in photodetection, results in noise
cancellation of the common noise, including thermal noise inher-
ited by both lasers from the cavity. This yields an output signal with
phase noise below that of the cavity thermal limit.
Figure 1(b) illustrates the primary noise contributions to
f
μ
and
their subtraction in the time domain. The two PDH-locked lasers
have frequency fluctuations dominated by two terms: the intrinsic
cavity thermal noise
σ
th
and the smaller residual noise of the PDH
lock
σ
PDH
that is related to technical servo limitations. Because of
significant overlap of the spatial modes of
ν
1
and
ν
2
in the F-P cav-
ity, there is strong amplitude and phase correlation between
σ
(
1
)
th
and
σ
(
2
)
th
. In the heterodyne, these noise terms largely subtract, as
shown in the bottom of Fig. 1(b). However, the PDH locking noise
σ
(
1
)
PDH
and
σ
(
2
)
PDH
arises from uncorrelated noise from the separate
laser locks and instead adds in quadrature in the heterodyne signal,
such that
σ
2
μ
=
(σ
(
1
)
PDH
)
2
+
(σ
(
2
)
PDH
)
2
.
The extent of the rejection of the correlated (common-mode)
noise can be estimated by considering the fractional frequency
stability that one laser inherits from the cavity, and extending
the argument to two lasers separated by
n
modes. The magni-
tude of the thermally driven fluctuations of a frequency mode
ν
of the cavity is directly linked to the fluctuations of the cavity
FSR, such that
σ
FSR
=
(
FSR
/ν)σ
ν
. Here we see that the fre-
quency fluctuations
σ
ν
of mode
ν
are ideally reduced by the
ratio of FSR
/ν
≈
10
−
4
. Similarly,
σ
n
×
FSR
=
(
n
×
FSR
/ν)σ
ν
,
where
n
×
FSR is the separation of any two modes of the cav-
ity [25]. Considering two lasers locked to modes separated by
5
×
FSR
=
118 GHz, the expected common rejection of fre-
quency fluctuations is 6
×
10
−
4
, which is equivalent to a reduction
of 20
·
log
(
118 GHz
/
193 THz GHz
)
≈−
64 dB in phase noise
power spectral density [25]. This estimate assumes perfect cor-
relation of thermal noise in the two cavity modes, and therefore
neglects the slight variations in cavity mode volume with wave-
length. But for two nearby axial modes, this approximation
sufficiently justifies how the phase noise of the mm-wave beat can
surpass the cavity thermal limit. It is then limited by the PDH lock-
ing noise of the lasers, which can be addressed through technical
advances.
In the experiment, the two PDH-locked lasers are mixed on a
commercial W-band photodetector and the resulting output is a
millimeter-wave (“output” in Fig. 1), having power of
≈
1 mW.
Here, we demonstrate millimeter-wave signals at 4
×
FSR and
5
×
FSR, with 94.5 GHz and 118.1 GHz carriers, respectively.
The phase noise of the millimeter-wave signals was measured using
cross correlation techniques to remove the uncorrelated noise of
reference local oscillators, as well as the mixer and amplifier noise
[32]. In brief, the photodetected signal was split with a
−
3 dB
waveguide coupler and each copy was mixed down to the RF using
harmonic mixers driven by independent commercial synthesiz-
ers. The two resulting baseband signals near 5 MHz were then
cross-correlated on a phase noise analyzer.
Research Article
Vol. 11, No. 11 / November 2024 /
Optica
1585
Fig. 1.
(a) Simplified schematic of the experiment, with pictures of the key components zoomed in. (b) Illustration of the mechanism of common-mode
rejection. Two signals (
ν
1
and
ν
2
) are indicated by their nominal frequencies (gray dashed lines) with their noise contributions (the thermal cavity noise of
each laser,
σ
(
1
)
th
and
σ
(
2
)
th
, as well as PDH locking noise,
σ
(
1
)
PDH
and
σ
(
2
)
PDH
, respectively) shown as continuous lines. The signal that results from their hetero-
dyning,
ν
RF
, is shown with the thermal cavity noise largely subtracted out. (c) Illustration of the two laser signals (red and blue) locked to two cavity modes
(dashed Gaussians), and heterodyned at 5 cavity FSRs apart, to generate a 118.1 GHz RF tone.
3. RESULTS
The result of the cross-correlation phase noise measurements of
the millimeter-wave signals is plotted in Fig. 2 (Cross-correlation
measurement details, Supplement 1, Note 2). We see three over-
laid traces of approximately the same phase noise level as the 1
FSR (23.6 GHz, blue), 4 FSR (94.5 GHz, yellow), and 5 FSR
(118.1 GHz, red) signals. This indicates that the phase noise of
any millimeter-wave signal of integer-multiple FSR frequency
can be generated and will inherit the phase noise of the PDH-
locked SIL lasers. The only limiting factor then is the power on the
high-speed photodetector, and hence the signal-to-noise ratio, of
the heterodyned signals as the frequency difference between the
two lasers is increased. The discrepancies in the phase noise of the
118.1 GHz signal versus the 23.6 GHz signal (near 10 kHz offset)
arise from the requirement of longer averaging times due to the
noise constraints of the cross-correlation reference signals.
Lastly and for comparison, on the same plot we have plotted (in
green) the cumulative noise contributions from the PDH servos
that we measure independently and add in quadrature. The various
noise contributions before summing can be seen in Supplement 1,
Note 3. These sources include the in-loop phase noise of each
SIL laser during PDH-lock operation, and the SNR floor of each
PDH servo loop. First, we measure the in-loop phase noise of the
error signal from the PDH reflection photodetector while the
laser is PDH-locked. Then we scale this noise appropriately with
the linewidth of the cavity and the slope of the PDH-lock error
signal [33] Similarly, we measure the electronic servo noise floor by
tuning the laser off resonance and measuring the phase noise of the
error signal output. This gives us the expected electronic noise floor
of the photodetector and servo in-loop while light is incident on
the detector but not on resonance. This is also scaled according to
the cavity linewidth and error signal slope. The result is four mea-
surements (two from each laser) that are summed in quadrature.
Fig. 2.
Phase noise plot of the 1 FSR apart (23.6 GHz, Blue), 4 FSR
apart (94.5 GHz, Yellow), and 5 FSR apart (118.1 GHz, Red) signals gen-
erated from heterodyning two self-injection-locked distributed feedback
lasers after PDH locking to two modes of the miniature F-P. In green, the
phase noise of the cumulative noise contributions is plotted, extrapolated
from the PDH-locked laser in-loop noise.
We find that the integrated phase noise of the green curve agrees
within a factor of 1.5 of the integrated phase noise of the 1 FSR,
4 FSR, and 5 FSR phase noise. Consequently, lower-phase-noise
lasers or higher PDH-lock gain would offer even greater noise
reduction.
In Fig. 3, we have plotted the free-running (without PDH
locking) SIL laser phase noise (blue) and the 118.1 GHz signal
phase noise (red), side-by-side, showing that
≈
37 dB of noise
reduction at 10 kHz offset is achieved by PDH locking, with AOM
and EOM feedback, to the F-P cavity. (For Allan deviation of the
Research Article
Vol. 11, No. 11 / November 2024 /
Optica
1586
Fig. 3.
Phase noise plot of the PDH-locked (yellow) versus unlocked
(blue) SIL lasers, both measured out of loop. In red, the heterodyned mil-
limeter wave at 5 FSR (118.1 GHz) separation is shown. In black-dashed
line, the F-P cavity thermal limit referenced from [31] is plotted.
out-of-loop SIL and mmWave, see Supplement 1, Note 1.) Here
we measured the free-running SIL noise by heterodyning the two
SIL lasers on an MUTC with
≈
10 GHz frequency difference. The
10 GHz signal is mixed down to DC and measured against a maser
reference on a phase noise analyzer. We make the assumption that
both free-running SIL lasers have similar but uncorrelated noise
profiles, such that this phase noise is simply twice (
+
3 dB) that of a
single SIL laser.
We also plotted the calculated thermal noise floor of the F-P
cavity in dashed-black [31]. Comparing the thermal limit to the
118.1 GHz millimeter-wave signal reveals that for offset frequen-
cies below 10 kHz, the phase noise of the millimeter-wave signal
surpasses the thermal-limited optical phase noise over a wide
range of Fourier frequencies. To further quantify the amount
of common-mode rejection exhibited, we independently mea-
sured the absolute (out-of-loop) phase noise of an individual
PDH-locked SIL laser (yellow in Fig. 3) by heterodyning with a
lower-phase-noise cavity-referenced laser. As expected, we see that
SIL laser noise follows the thermal limit of the F-P cavity up to
about 10 kHz. At higher frequencies, the laser noise is limited by
PDH servo gain and bandwidth.
The difference between the out-of-loop optical phase noise and
the mm-wave phase noise is the amount of noise common to both
lasers and hence subtracted (rejected) in the heterodyne signal,
which is both the thermal noise of the cavity and vibration-induced
noise of the cavity. Thus the mm-wave signal here gains 22 dB of
noise rejection at 10 Hz offset, due to both optical references being
PDH-locked to the same cavity.
To put our result into context, we have included a survey of the
reported phase noise of state-of-the-art photonic millimeter-wave
synthesis. As seen in Fig. 4, our SIL and PDH framework allows for
exceptionally low-noise millimeter-wave synthesis, largely falling
well below commercial products and existing photonic-based
sources up until the servo bump at around 300 kHz. This does not
tell the full story, however, as other millimeter-wave generators
rely on significantly more complex systems or non-integratable
components, to achieve lower and similar phase noise.
For example, the lowest phase noise achieved and plotted in
red squares, incorporates full optical frequency division using an
octave spanning, titanium-doped sapphire, bulk-optic frequency
Fig. 4.
Phase noise plot of the photonically generated millimeter-wave
landscape scaled to 118.1 GHz [14,17,20,27].
comb and a filtering etalon [17]. The power required to run such
a system is thus significantly higher than the one in this work. The
lowest photonic-chip-based mm-wave noise (blue stars) falls in line
with the results we present, yet they require a microcomb to achieve
OFD [27]. In addition to the microcomb, this requires a more
complex locking scheme. A more recent work from the same group
has offered further simplification by using OFD with an injection-
locked comb [34]. With the exception of additional spurious noise,
these latest results are still comparable to what we present here, with
noticeably reduced phase noise and a servo bump extended out to
500 kHz. Significantly, we have shown that such phase noise levels
can be achieved without OFD using simple SIL lasers that require
low input currents (200 mA to drive the lasers) and have a clear
path toward chip integration.
The phase noise survey also includes other mm-wave synthe-
sizers that employ self-injection locking with diode lasers (gray
triangles) [14] and Brillouin lasers (orange squares) [20]. In the
dual-wavelength Brillouin architecture, a 75-m-long fiber spool is
used as a common cavity for self-injection locking two lasers.
In our data of Fig. 4, we see that there is excess noise arising from
the servo bumps spanning 100 kHz to 1 MHz. This noise is attrib-
uted to the phase roll-off and limited gain of the laser control servo
electronics. To mitigate this noise, one could implement servo con-
trol electronics with higher phase roll-off or an electro-optic modu-
lator as an additional actuator [35].
There are additional spurious tones at 100–400 Hz in the
out-of-loop PDH-locked laser phase noise of Fig. 3. These are also
evident, at reduced amplitude, in the phase noise of the 118.1 GHz
signal. Presumably, these arise from mechanical noise of the
optomechanical stages that the lasers and chips reside on, as well as
excess fiber noise. Additionally, some of these peaks likely originate
from AM-PM conversion due to the relative intensity noise of the
lasers.
4. CONCLUSION AND OUTLOOK
In conclusion, we have shown a simplified, compact way to gen-
erate low-phase-noise millimeter-wave carriers, by transferring
the noise of stable optical references to any integer multiple of the
F-P cavity FSR. Importantly, through common-mode rejection,
we surpass the thermal limit of the reference cavity. In doing so,
we have shown millimeter-wave phase noise of
−
118 dBc
/
Hz
Research Article
Vol. 11, No. 11 / November 2024 /
Optica
1587
at 10 kHz offset, regardless of carrier frequency. This perform-
ance is better than any chip-scale photonic mm-wave generation
to date, and is within 5 dB the highest-performing full-OFD
millimeter-wave source.
In addition to the phase noise performance, the low complexity
and compact form factor of this experiment both lend themselves
towards full integration. For example, with advances of micro-F-P
cavities [24,25,36], integrated SIL lasers, and on-chip MUTC
photodetectors [22,37], the approach we present can be inte-
grated onto a single chip. And in comparison to more complex
OFD schemes [26,27], we show an attractive option to reduce the
number of integrated components and realize on-chip, low-noise
mm-wave generation with robust and turn-key operation.
Funding.
National
Institute
of
Standards
and
Technology
(80NM0018D0004); Defense Advanced Research Projects Agency GRYPHON
program (HR0011-22-2-0009).
Acknowledgment.
W.G., I.K., K.J.V, J.E.B., F.Q., and S.A.D. conceived
the experiment and supervised the project. W.G., I.K., and S.A.D. wrote the
paper with input from all authors. W.G., I.K., and A.L. built the experiment and
performed the mm-wave experiment. D.L., T.N., and Y.L. provided mm-wave ref-
erence sources and input regarding the cavity and cross-correlation measurements.
M.L.K and C.A.M. built the cavity and provided information regarding the cavity.
J.G., L.W., W.J., K.J.V, and J.E.B provided the lasers and spiral microresonators, as
well as input regarding the operation of the lasers.
Disclosures.
The authors declare no conflicts of interest. Commercial equip-
ment and trade names are identified for scientific clarity only and do not represent
an endorsement by NIST.
Data availability.
Data underlying the results presented in this paper are not
publicly available at this time but may be obtained from the authors upon reason-
able request.
Supplemental document.
See Supplement 1 for supporting content.
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