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Low phase noise THz generation from a ﬁberreferenced Kerr microresonator soliton comb

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Naoya Kuse 1,2 ✉, Kenji Nishimoto3, Yu Tokizane1, Shota Okada3, Gabriele Navickaite4, Michael Geiselmann4,
Kaoru Minoshima 1,5 & Takeshi Yasui 1

THz oscillators generated via frequency-multiplication of microwaves are facing difﬁculty inachieving low phase noise. Photonics-based techniques, in which optical two tones aretranslated to a THz wave through opto-electronic conversion, are promising if the relative
phase noise between the two tones is well suppressed. Here, a THz (≈560 GHz) wave with alow phase noise is provided by a frequency-stabilized, dissipative Kerr microresonator soliton
comb. The repetition frequency of the comb is stabilized to a long ﬁber in a two-wavelength
delayed self-heterodyne interferometer, signiﬁcantly reducing the phase noise of the THz
wave. A measurement technique to characterize the phase noise of the THz wave beyond thelimit of a frequency-multiplied microwave is also demonstrated, showing the superior phasenoise of the THz wave to any other photonic THz oscillators (>300 GHz).

1 Institute of Post-LED Photonics, Tokushima University, 2-1, Minami-Josanjima, Tokushima, Tokushima 770-8506, Japan. 2 PRESTO, Japan Science andTechnology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan. 3 Graduate School of Sciences and Technology for Innovation, Tokushima
University, 2-1, Minami-Josanjima, Tokushima, Tokushima 770-8506, Japan. 4 LIGENTEC SA, EPFL Innovation Park L, Chemin de la Dent-d’Oche 1B,
Switzerland, CH-1024 Ecublens, Switzerland. 5 Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka,
Chofu, Tokyo 182-8585, Japan. ✉email: kuse.naoya@tokushima-u.ac.jp

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pectral purity of electromagnetic ﬁelds, which is quantiﬁedby phase noise, is one of the most important parameterswhen the electromagnetic ﬁelds are used as oscillators. A
distinguished example in the optical domain is ultra-stable, lownoise continuous-wave (CW) lasers for optical clockworks1,2. In
the microwave domain, low phase noise oscillators have been
widely used both in the scientiﬁc and industrial world suchas radars, communications, radio astronomy, and particle
accelerators3–5. Recently, the demand for oscillators in the mm
and THz ranges has been expanded mainly for next-generation
communication (5G and 6G), including radars, molecular clocks,
and wireless communications6–9.
Optical frequency combs10 based on mode-locked ﬁber orsolid-state lasers coherently connect the optical and microwave
frequency through photodetection, where ultra-low phase noiseof the repetition frequency (frep: repetition frequency) is faithfullytransferred to microwaves11–13, reaching the shot noise ﬂoor of−170 dBc/Hz at the 1 kHz frequency offset with 1/f (f: frequency
offset from a carrier) slope for a 12 GHz carrier12. However, ﬁber
combs and solid-state laser combs are not suitable for the generation of mm and THz waves owing to the inherently narrowcomb mode spacings (<1 GHz). On the other hand, otherphotonics-based methods such as optoelectronic oscillators(OEOs)14,15 and heterodyning of two CW lasers16–20 are suitable
for the generation of mm and THz waves. In particular, heterodyne methods can be easily applied to a higher frequency. Amongthe heterodyne methods, two Brillouin lasers from a single cavity
produce the small relative phase noise of the two CW lasers18,19.
Also, two self-injection locked lasers from high-Q cavities havebeen employed for low-phase-noise W-band (92 GHz) radar20.
Owing to the advent of integrated optical frequency combs
based on dissipative Kerr microresonator soliton combs (Kerr
combs)21,22, the generation of mm and THz waves from Kerr
combs has been explored23–25 to outperform the above heterodyne methods using two CW lasers. The free spectral range (FSR)
of microresonators used to generate Kerr combs can be easily
more than 100 GHz, which is suitable for the generation of mm
and THz waves through opto-electronic conversion by photodetectors. Moreover, Kerr combs are a mode-locked state, where adouble balance of gain and loss as well as nonlinearity and dispersion exists, providing low-noise, coherent, ultra-short pulses.
A mm wave (100 GHz) has been generated from a 100-GHz, freerunning Kerr comb, showing a strong coherence between the
comb modes24. To improve the phase noise, a 300 GHz Kerr
comb is stabilized to two Brillouin lasers, where optical frequency
division from 3.6 THz (=frequency separation of the two Brillouin lasers) to 300 GHz (=frep of the Kerr comb) is utilized,
suppressing the phase noise by 40 dB in the wide range of frequency offsets for a 300 GHz carrier25. However, the method
based on Brillouin lasers requires temperature stabilization(<10 mK temperature stability), operation in vacuum, and additional two phase-locked loops to suppress the mode-hopping of
the Brillouin lasers26. Also, two narrow-linewidth CW lasers are
required in addition to the Kerr comb. Moreover, owing to
the coupling between the laser dynamics and cavity ﬂuctuation,
the phase noise of the Brillouin laser at the low frequency offsets
is unsatisfactory, limiting the phase noise of the 300 GHz wave at
the low frequency offsets. Another method to stabilize the frep ofKerr combs is based on a two-wavelength delayed self-heterodyne
interferometer (TWDI)27,28, in which a long ﬁber in an imbalanced Mach–Zehnder interferometer (i-MZI) works as a reference. TWDI is the extension of i-MZIs with a long ﬁber, which
has been used to stabilize a CW laser29 and comb modes of a fceostabilized frequency comb30, to the two different wavelengths,
enabling the detection of the phase noise of frep31. In the method,
the phase noise of the frep is measured in a self-referencing way
2

owing to the time delay between the two arms in the i-MZI,
allowing simple and robust operation of the stabilization system.
Furthermore, the phase noise limit at the frequency offsets below
10 kHz set by the ﬁber length ﬂuctuation can be minimized30,32,
compared to the system using a Kerr comb and two Brillouinlasers25. However, despite the importance of the THz oscillator
and advantages of the TWDI over the system using a Kerr comb
and two Brillouin lasers25, TWDIs have not been utilized for THz
waves generation from a Kerr comb, yet.
In this report, we demonstrate the generation of a low phasenoise THz (≈560 GHz) wave from a frep (≈560 GHz) stabilized
Kerr comb. The low phase noise is obtained by stabilizing theTHz Kerr comb to a TWDI, where the phase noise of the frep is
extracted by mixing the phase noise of the two comb modes atdifferent frequencies and feeding-back to the pump CW laser.
The stabilization suppresses the phase noise of the frep by morethan 40 dB in the wide range of frequency offsets. Due to the lackof established methods to characterize carriers with THz frequency and low phase noise, we also propose and develop amethod for the measurement of the phase noise of the THz wave
beyond the limit of conventional microwave technologies, where
two low noise THz waves to be characterized are down-converted
to a microwave at a Schottky barrier diode (SBD) by the squarelaw detection. With the generation and measurement of the low
noise THz wave, we show that the phase noise of the stabilized
frep in the THz regime is transferred to the THz wave, exhibiting
the superior phase noise of the THz wave to any other photonic
THz (>300 GHz) oscillators.
Results
Architecture for the THz generation. A basic architecture forthe generation of a low phase noise THz is shown in Fig. 1. There
are three main elements: (1) Kerr comb, (2) detection and stabilization of the frep, and (3) THz wave generation. A Kerr comb
is generated from a high-Q Si3N4 microresonator. The phasenoise of the frep is detected in the optical domain by using a
TWDI and referencing a long ﬁber in the TWDI as explained in
the following (see a photo in Fig. S1). The detected phase noise of
the frep works as an error signal for a feedback loop, which is
closed by feeding back to the Kerr comb. After suppressing thephase noise of the frep, two comb modes of the Kerr comb are
extracted by an optical ﬁlter, followed by a uni-traveling-carrier(i) Kerr comb(ii) Measurement of
frep phase noise(iii) THz generation

Fig. 1 Conceptual schematic of the generation of a low phase noise THz
wave. (i) A Kerr comb is generated from a microresonator. (ii) The phasenoise of the frep of the Kerr comb is stabilized to a long ﬁber in a twowavelength delayed self-heterodyne interferometer (TWDI) through afeedback loop. (iii) The two comb modes of the frep-stabilized Kerr comb
are extracted by an optical ﬁlter, followed by an uni-traveling-carrier
photodiode (UTC-PD) to generate a THz wave.

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Fig. 2 Low phase noise THz genearation and characterization. a Schematic of the experimental setup. The dashed blue (red) squares show the setups forcomb 1 (comb 2) and TWDI 1 (TWDI 2). The dashed purple squares show the setup for the generation and characterization of a THz wave. AOM: acoustooptic modulator, SBD: Schottky barrier diode. b Illustration of the working principle of the TWDI. Pairs of single comb modes with (solid line) and without(dotted line) delay are photodetected, generating signals with the phase noise PSDs of ∣H(if)∣2{Lceo(f) + n2Lrep(f)} and ∣H(if)∣2{Lceo(f) + (n + Δ)2Lrep(f)}.
By mixing the two signals, a DC signal with the phase noise PSD of ∣H(if)∣2 ⋅ Δ2Lrep(f) is generated, which is used as an error signal. c Illustration of theworking principle of the characterization of the phase noise of the THz. Four comb modes from combs 1 and 2 are directed into an UTC-PD, generating two
THz waves with the carrier frequencies of frep1 and frep2. The two THz waves are squared-law-detected at a SBD, generating a microwave with the phasenoise of the sum of the two THz waves.

photodiode (UTC-PD). The optical ﬁlter is required to avoid thedestructive interference between the comb modes unless thedispersion of the Kerr comb is compensated. The UTC-PD
converts the optical two tones to a THz wave, whose frequency
corresponds to the spacing of the two tones. The phase noise andfrequency stability of the THz wave inherit those of the frep of theKerr comb, i.e., relative phase noise and frequency stability
between the two comb modes, providing the generation of a low
phase noise THz wave from the frep-stabilized Kerr comb.
Experimental setup. Figure 2a shows an experimental setup not
only to generate a low phase noise THz wave but also to measure
the phase noise and frequency stability of the THz wave. Two
Kerr combs (combs 1 and 2) are generated by using two independent systems (detail is shown in the “Methods” section and
Supplementary Note 1), in which a single-longitudinal CW laser(external cavity diode laser: ECDL) is coupled into a high-Q Si3N4
microresonator33. The Kerr comb passes through a bandstop
ﬁlter to reject the residual pump CW laser. The repetition frequencies of combs 1 and 2 (frep1 and frep2) are approximately
560 GHz. The Kerr comb is split into two. One is directed to a
TWDI27, and the other is used for THz generation. TWDI consists of an i-MZI with two outputs followed by optical bandpass
ﬁlters. A large time delay between the two arms in the i-MZI is
employed for the self-referencing by installing a long ﬁber (≈20,
80, 100, and 110 m in the experiments). An acousto-optic
modulator (AOM) is also installed in the i-MZI for the selfheterodyne detection. The optical bandpass ﬁlters (OBPFs) selecta pair of comb modes at a speciﬁc frequency (n and (n + Δ)th in
Fig. 2b), which are directed into photodetectors, generating
delayed-self heterodyne signals. More details of the experimental
setup of the TWDI are shown in the method section and Fig. S1.

The delayed self-heterodyne signals show the phase noise PSDs of
the nth comb mode (∣H(if)∣2{Lceo(f) + n2Lrep(f)}) and the (n + Δ)
th comb mode (∣H(if)∣2{Lceo(f) + (n + Δ)2Lrep(f)}). Here, H(if),Lceo(f), and Lrep(f) are the transfer function of the i-MZI (see inthe method section) and phase noise PSDs of the carrier-envelope
offset frequency and frep of the Kerr comb, respectively. By mixing
the two delayed self-heterodyne signals, a DC signal with thephase noise PSD of ∣H(if)∣2 ⋅ Δ2Lrep(f) is obtained, while cancelingout Lceo(f) owing to the common-mode rejection. Since the DC
signal contains Lrep(f) only with coefﬁcients of H(if) and Δ, a
feedback loop to make the DC signal ﬁxed at zero reduces Lrep(f).
Throughout the experiments in this report, Δ is ﬁve (the +1st and−4th for comb 1 and +2nd and −3rd for comb 2). In theexperiments, the loop is closed by feeding back to the pumpcurrent of the pump CW laser and PZT in the pump CW laser
cavity for fast and large-range control, respectively, modulating
the frequency of the pump CW laser. To characterize the THz
wave, two comb modes from combs 1 and 2 (four comb modes intotal) are extracted by an optical ﬁlter (4000 s from Finisar)(Fig. 2c, top left) and input into a UTC-PD with an integrated
antenna (IOD-PWAN-13001-2 from NTT Electronics). THz
waves with the carrier frequencies of frep1 and frep2 (Fig. 2c, top
right) propagate in free space. The two THz waves are focused
onto a SBD (WR1.9ZBD from Virginia Diodes Inc.), generatinga microwave with the carrier frequency of ∣frep1 − frep2∣(≈1.26 GHz) (Fig. 2c, bottom) through the square-law detection.
The phase noise and frequency stability of the microwave are thesums of those of the two THz waves, which inherit the phasenoise and frequency stability of the frep of the two Kerr combs.
However, owing to the use of a single UTC-PD for the generationof the two THz waves, the correlated phase noise between the two
THz waves originated in the opto-electronic conversion process

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(a)

(c)

(e)

(b)

(d)

(f)

Fig. 3 Optical spectra and RF spectrum. Optical spectra of combs 1 (a) and 2 (b) before the bandstop ﬁlter and ampliﬁed optical spectra of combs 1 (c)and 2 (d) after the bandstop ﬁlter. e Optical spectrum of four comb modes (blue curve from comb 1 and red curve from comb 2) used for THz waves
generation. f RF spectrum of the microwave generated from the SBD. Resolution bandwidth (RBW) for a–d is 1 nm. RBW for e is 0.02 nm. RBW for f is
100 kHz.

at the UTC-PD such as the amplitude-to-phase noise conversion
and ﬂicker noise cannot be included. Therefore, the phase noisecharacterization presented here shows the lower limit of the phasenoise of the THz wave. Alternatively, the two Kerr combs can bedirected to two independent UTC-PDs and downconverted by afundamental mixer to cover the phase noise arising in the photodetection process. Owing to the availability of the UTC-PD in
our lab, we use a single UTC-PD. More details about the generation and characterization of the THz wave are shown in themethod section and Supplementary Note 1.
Experimental results. Figure 3a, b shows the optical spectra ofcombs 1 and 2 before the bandstop ﬁlters. The smooth sech2
envelope with the comb mode spacing equal to the FSR of the
microresonator indicates the Kerr comb is a single soliton state.
After rejecting the strong residual pump CW laser by the bandstop ﬁlter, the Kerr combs are ampliﬁed (not shown in Fig. 2a) by
an erbium-doped ﬁber ampliﬁer (EDFA) for the following
experiments as shown in Fig. 3c, d for combs 1 and 2, respectively. The optical signal-to-noise ratio (OSNR) of the comb
modes is signiﬁcantly degraded by the ampliﬁed spontaneousemission (ASE) during the ampliﬁcation down to about 28 dB at
the resolution bandwidth (RBW) of 1 nm for the comb modes.
The OSNR is one of the limiting factors of the sensitivity of theTWDI, which is further discussed later and in Supplementary
Note 2. Figure 3e shows the comb modes used for the THz waves
generation. The optical power of each comb mode is about 8 mW,
and 32 mW in total is input into the UTC-PD. The THz waves
are down-converted to a microwave by mixing the two THz
waves at the SBD by the square-law detection. The RF spectrumof the microwave is shown in Fig. 3f. The SNR of the microwave
is about 58 dB at the RBW of 100 kHz, resulting in a measurement noise ﬂoor of −108 dBc/Hz.
The repetition frequencies of combs 1 and 2 are stabilized to along ﬁber in TWDIs 1 and 2. The imbalanced ﬁber length for
TWDIs 1 and 2 are 100 and 80 m, respectively. The ﬁber length isselected such that the phase noise around the 10 kHz frequency
offset is optimized. RF spectra of the down-converted microwave
are shown in Fig. 4a. When the feedback loops both for combs 1
and 2 are closed, the phase noise close to the carrier is suppressed,
4

showing the signiﬁcant narrowing of the linewidth. A servo bumpis observed around the 200 kHz frequency offset. The singlesideband (SSB) phase noise PSD of the down-converted signal(Lmw(f)) is shown in Fig. 4b (red curve), which is measured by anelectric spectrum analyzer (N9030A from Keysight). Comparedwith the phase noise PSDs of the frep of free-running combs 1(blue in Fig. 4b) and 2 (green in Fig. 4b), the phase noise issuppressed by more than 40 dB at the frequency offsets below
10 kHz, reaching −49, −77, −99, −95, and −108 dBc/Hz at thefrequency offsets of 100 Hz, 1 kHz, 10 kHz, 100 kHz, and 1 MHz,
respectively. The integrated timing jitter from 100 Hz to 1 MHz
can be estimated as 14 fs from the phase noise PSD. Note that
Lmw(f) is the sum of the phase noise PSDs of frep1 and frep2(Lrep1(f) and Lrep2(f)), indicating that the phase noise of a single
THz wave is better than the shown phase noise.
Not only the short-term stability (i.e., phase noise) but also thelong-term stability is improved by locking the frep to the longﬁber. Figure 4c shows the frequency drift of the down-converted
microwave. Without the locking, the frequency drift of 6.6 MHz
for 1 h is observed, whilst the locking suppresses the frequency
drift down to 120 kHz. In both cases, the linear drift would becaused by the temperature ﬂuctuation (<0.1 K in our lab for 1 h).
However, the inﬂuence is more signiﬁcant (×55) for the freerunning Kerr comb, because the temperature ﬂuctuation couples
various factors such as ﬂuctuations of FSR, detuning, and pump
power. On the other hand, the frequency drift with thestabilization to the TWDI just follows the ﬁber length ﬂuctuation
if the feedback gain is large enough. When the linear drift isremoved by signal processing, the standard deviation also shows
an improvement from 390 to 20 kHz. Fractional frequency
instability is also evaluated from the results of the frequency drift(Fig. 4d). The fractional frequency instability is improved by twoorders of magnitude, reaching 10−10 at the 0.1 s averaging time,
which is gradually degraded owing to the ﬂuctuation of the ﬁber
length in the TWDI. The frequency instability of 1.4 × 10−11 at
1 ms averaging time is also estimated from the phase noise PSD
in Fig. 4b.
In Fig. 5a, Lmw(f) is compared with the sum of the out-of-loop
phase noise PSDs of the stabilized frep1 and frep2, which aremeasured by using the two TWDIs (see Supplementary Note 2).

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(a)

(c)
1 hour100 kHz(b)(d)

Fig. 4 Phase noise spectra and frequency instability of the THz wave. a RF spectra of the down-converted microwave with (red curve) and without (bluecurve) locking, measured with the RBW of 3 kHz. b Single-sideband (SSB) phase noise power spectral density (PSD) and timing jitter of the downconverted microwave (red curve) and that of the repetition frequency of free-running combs 1 (blue curve) and 2 (green curve) measured by the TWDI.
c Frequency drift of the down-converted microwave with (red curve) and without (blue curve) locking. The inset shows the magniﬁed frequency drift of thedown-converted microwave with locking. d Frequency stability of the down-converted microwave calibrated at 560 GHz with (red line and circle) andwithout (blue line and circle) locking.

Fig. 5 Phase noise limit. a Single-sideband (SSB) phase noise power
spectral densities (PSDs) of the microwave down-converted from the two
THz waves (red curve) and the sum of the out-of-loop phase noise PSDs of
frep1 and frep2 (blue curve). The dashed line shows the measurement noise
ﬂoor for the microwave limited by the generated THz power. b In-loop
phase noise PSD of the stabilized frep of comb 1 (red curve). c Fiber noise
limit (red curve) and theoretical thermal noise of the ﬁber39–41 (gray line).
d Optical signal-to-noise ratio (OSNR) limit of the TWDI (red curve). The
blue curves in b–d are the out-of-loop phase noise PSD of the stabilized frepof comb 1.

Here, the in-loop phase noise PSD of the stabilized frep is deﬁned
as the phase noise PSD of the error signal divided by Δ2∣H(if)∣2of the TWDI, which is used for the stabilization. For themeasurement of the out-of-loop phase noise PSD of frep, another
TWDI is used, and out-of-loop phase noise PSD of the stabilized
frep is deﬁned as the phase noise PSD of the error signal divided
by Δ2∣H(if)∣2 of the other TWDI. Although Lmw(f) overlaps withthe sum of the out-of-loop phase noise PSDs of frep1 and frep2 at
the wide frequency offsets, a deviation is observed at thefrequency offsets below 300 Hz. The excess noise can beoriginated from the opto-electronic conversion at the UTC-PD.
In addition, since a single UTC-PD is used, the excess phase noise
may be underestimated owing to the correlation of the optoelectronic conversion process within the UTC-PD. Moreinvestigation of the excess noise such as the amplitude-to-phasenoise conversion and ﬂicker noise from the UTC-PD with THz
bandwidth is left for future research. Above the frequency offset
of 400 kHz, Lmw(f) is limited by the measurement noise ﬂoor. In
the following, we investigate the limit of the phase noise of thestabilized frep to indirectly investigate the limit of the phase noiseof the THz wave. Figure 5b shows the out-of-loop (the blue curve)
and in-loop (the red curve) phase noise of the stabilized frep1. The
out-of-loop phase noise of the stabilized frep1 follows the in-loop
phase noise at the frequency offsets above the 10 kHz. To
decrease the phase noise at this range, Kerr combs withintrinsically small phase noise are required, which would be
realized by operating in the quiet points34, optimizing thedispersion of microresonators35, and using laser coolingtechniques36–38. Alternatively, a shorter ﬁber can be used in the
TWDI to increase the feedback gain, at the expense of theincrease of the ﬁber noise limit and OSNR limit of the TWDI.
Figure 5c shows the limit of the ﬁber noise. Although the thermal
noise of the ﬁber is far below39–41 (the gray curve in Fig. 5c), theﬁber is inﬂuenced by acoustic noises. The ﬁber noise is prominent
at the frequency offsets below 1 kHz. Currently, the i-MZI in the
TWDI is just enclosed in an aluminum box with a thickness of 5mm. To reduce the ﬁber noise, more delicate handling of the ﬁbersuch as putting into an enclosure with acoustic damping foam31
and low vacuum environment42 on vibration immune table, atthe cost of complexity, is useful. Another method to reduce theﬁber noise limit (∝L−1, L: ﬁber length difference in the i-MZI) is
to employ a longer ﬁber. However, the use of a longer ﬁber
decreases the feedback gain/bandwidth, increasing the in-loop
limit. Figure 5d shows the OSNR limit of the TWDI, which isdetermined by the noise generated from the photodetection andsubsequent electric components. At the photodetection, white

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noise is generated from the limited OSNR of the comb mode,
which shows the OSNR limit with a f12 slope after divided by
Δ2∣H(if)∣2. The OSNR limit is inﬂuential at the frequency offsets
below 10 kHz. To lower the OSNR limit, the OSNR of the comb
mode that is used in the TWDI needs to be increased. Currently,
the OSNR is limited by the ASE from the EDFA used aftergenerating the Kerr comb. Overcoupled-microresonator would
provide larger comb mode power43,44, which reduces the ASE.
Alternatively, the comb mode can be ampliﬁed by using injection
locking, which provides more than 50 dB OSNR at the RBW of
1 nm45. In another way (or combined with injection locking), theuse of largely separated comb modes also reduces the sensitivity
limit owing to the larger factor of Δ. With a ﬁxed OSNR and Δ, alonger ﬁber reduces the OSNR limit, however, at the cost of the
reduction of the feedback gain/bandwidth, increasing the in-loop
limit. Since both the ﬁber noise limit and OSNR limit would be
improved by using a longer ﬁber, the better phase noise at the low
frequency offset and the better frequency instability would beobtained until the in-loop limit is reached. More details for thisparagraph are shown in Supplementary Note 2.
The obtained phase noise is compared with literature reporting
the generation of >100 GHz waves from Kerr combs in Fig. 6. Fora fair comparison, the phase noise is scaled to 560 GHz. The
phase noise of the frep of the free-running 560 GHz Kerr comb
(comb 1) is much better than that of the 100 GHz Kerr comb
when scaling to 560 GHz is considered24. Smaller free-runningphase noise is important to achieve the lower phase noise with thestabilization because of the limited feedback gain. Whenstabilized, our result is compared with the system using a Kerr
comb and two Brillouin lasers25. Our phase noise is slightly betterat the frequency offsets of >10 kHz. At the frequency offsets
below 10 kHz, which is essential for e.g., Doppler radar20, ourresults show a superior (more than 20 dB better) performancewith a simple aluminum enclosure for the TWDI. On thecontrary, in the system using a Kerr comb and two Brillouinlasers25, despite a careful enclosure (100 mTorr in a vacuum
chamber) for the Brillouin lasers, the obtained phase noise at thefrequency offsets is limited by the references, i.e., relative phasenoise between two Brillouin lasers, which might be difﬁcult tofurther improve. Also, again note that our system is simpler andmore robust as explained in the introduction.
Conclusions
We have generated a low noise THz (≈560 GHz) wave, which has
been characterized by a measurement system for the low noise
THz wave. The THz wave has been generated from a Kerr comb,
whose frep has been stabilized to a long ﬁber in a TWDI, whichallows the detection of the phase noise of the frep in a selfreferenced way. To characterize the phase noise and frequency
stability of the THz wave, we employed a measurement system,
which eliminates the use of a frequency-multiplied microwave asa reference, thus, enabling the phase noise characterization
beyond the limit of the conventional microwave technologies.
With the generation and measurement of the low noise THz
wave, we showed the SSB phase noise PSD of −49, −77, −99,
−95, and −108 dBc/Hz at the frequency offsets of 100 Hz, 1 kHz,
10 kHz, 100 kHz, and 1 MHz, respectively. However, note thatthe measured phase noise is blind to the correlated excess noise
between the two THZ waves arising in the opto-electronic conversion process at the UTC-PD, and further study of the excess
noise of the UTC-PD with the THz bandwidth such as theamplitude-to-phase conversion and ﬂicker noise is required.
According to an out-of-loop measurement of the SSB phase noise
PSD of the frep-stabilized comb 1, the SSB phase noise PSD of theTHz wave (LTHz(f)) at the 10 kHz frequency offset could be−105 dBc/Hz (see Figs. 5b and S3a). The obtained phase noise islimited by the in-loop noise (>10 kHz frequency offset), ﬁber
noise, and OSNR of the comb modes (<10 kHz frequency offset).
In addition to the careful handling of a long ﬁber, the use ofwidely-separated comb modes with high OSNR could improve
the phase noise, in which injection locking of two CW lasers to
the comb modes would be effective. In regard to measurement,
the noise ﬂoor is more than 10 dB better than the obtained phasenoise for the frequency offset of less than 100 kHz. When asmaller noise ﬂoor is required, the down conversion toa microwave from two THz waves can be realized by using afundamental mixer, which improves the conversion efﬁciency.
Although more progress would be required, the demonstrated
system would be more integrated using Si photonics technologies.
In particular, the rapid progress of the development of low loss,
chip-scale waveguides would remove the use of a 100 m ﬁber46,47.
The demonstrated system for the generation and characterizationof low noise THz waves advances THz-based technologies forradars, wireless communications, and analog-digital converters in
the era of 5G and 6G.
Methods

Fig. 6 Comparison with other Kerr combs scaled to 560 GHz. Singlesideband (SSB) phase noise power spectral densities (PSDs) of 560 GHz
carriers generated from free-running Kerr combs reported in the ref. 24(light blue triangle) and this work (red square). SSB phase noise PSDs of
560 GHz carriers generated from stabilized Kerr combs reported in theref. 25 (light red curve) and this work (red curve). The phase noise shownby the blue curve is estimated from the measurement by a TWDI, insteadof actually generating a 560 GHz carrier. When a 560 GHz carrier isgenerated, phase noise will see the white noise ﬂoor similar to the red
curve. The red curve is sum of the two comb (Lrep1(f) and Lrep2(f)).
Therefore, the phase noise of a single 560 GHz carrier would be a few dB
better.
6

Kerr comb generation. An external cavity diode laser is used as a pump CW laser.
The pump CW laser passes a dual-parallel Mach-Zehnder modulator (DP-MZM)
for the fast scanning of the frequency of the pump CW laser, which is used toovercome the fast thermal dynamics of the microresonator induced when a chaotic
comb transitions to a Kerr comb27. The DP-MZM is operated in a carriersuppressed single sideband mode by applying an RF with a 90° phase difference tothe two nested MZM and appropriately adjusting the phase bias. The frequency of a
voltage-controlled oscillator (VCO, fvco) is controlled by a step function from anarbitrary waveform generator (AWG) to change the fvco. After generating the Kerrcomb, the AWG is swapped to a DC power supply to reduce the phase noise of theVCO. Otherwise, an excess phase noise onto the pump CW laser is observed. The
output from the DP-MZM is ampliﬁed by an EDFA, followed by an OBPF to reject
the ASE from the EDFA. The pump CW laser with the optical power of 200 mW is
coupled into a bus waveguide through a lensed ﬁber with an insertion loss of below
3 dB. The microresonator is made of Si3N4 and fabricated by the damascene processwith the quality factor of more than >1 × 106. After generating the Kerr comb, theresidual pump CW laser is rejected by an optical bandstop ﬁlter, followed by an
EDFA to amplify the optical power up to 160 mW. The ampliﬁed Kerr comb is split
into two, which are directed to the setup for the TWDI and THz generation/
characterization, respectively. The experimental setup is shown in Fig. S1.

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COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-022-01100-0

TWDI. The Kerr comb is input into an i-MZM. Two AOMs (+80 MHz and−80 MHz shift, respectively) are used in both arms of the i-MZM to avoid theinterference between the carrier from one arm and the residual carrier from the otherarm. A long ﬁber (20, 80, 100, and 110 m in the experiments) is installed. A PZT is
attached onto a ﬁber to control the delay between the two arms, which is used tocontrol the relative phase between two inputs of the mixer. The two outputs from thei-MZI pass through an OBPF to extract a pair of comb modes. In the experiments, the+1st and −4th comb modes of comb 1 and +2nd and −3rd comb modes of comb 2
are used for the TWDI. The extracted comb modes are photodetected, generating RF
signals with the carrier frequency of 160 MHz. After the RF signals are ﬁltered andampliﬁed, the RF signals are mixed, followed by a low pass ﬁlter to extract a DC
signal, which shows the phase noise of the frep. When the frep is stabilized, thefrequency of the comb is modulated by controlling the pump current and PZT of thepump CW laser according to the error signal. The pump current is used for the fast,
but narrow-range control, while the PZT is used for the slow, but wide-range control.
The transfer function of the iMZI used in the TWDI can be expressed as48
jHðif Þj2 ¼ 4sin2 ðπτf Þð1ÞHere, τ is the time delay between the two arms of the i-MZI. The transfer function
shows the scaling of f2.
THz generation and characterization. Combs 1 and 2 are combined by an optical
coupler. The four comb modes (two modes from each comb) are extracted by awaveshaper (4000 s from Finisar), which are ampliﬁed by an EDFA to 32 mW. The
power of the four comb modes before the waveshaper is carefully adjusted such thatthe power of the four comb modes after the EDFA become equal. The ampliﬁed
comb modes are directed through a UTC-PD, generating two THz waves. Although
the power of the two THz waves is not measured, power of each THz wave is likely
to be around −26 dBm according to the datasheet. The two THz waves are collimated and focused onto a SBD, where the two THz waves are down-converted intoa microwave through the square-law detection. The microwave is ﬁltered by an RF
low-pass ﬁlter and ampliﬁed by RF ampliﬁers. The phase noise of the microwave ismeasured by an electric spectrum analyzer. To measure the frequency of the
microwave, the microwave is further down-converted by mixing with a local
oscillator, followed by a low pass ﬁlter. The experimental setup is shown in Fig. S1.

Data availability
The data that support the ﬁndings of this study are available from the corresponding
author upon reasonable request.

Received: 13 May 2022; Accepted: 22 November 2022;

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Correspondence and requests for materials should be addressed to Naoya Kuse.
Peer review information Communications Physics thanks the anonymous reviewers fortheir contribution to the peer review of this work.
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Acknowledgements
G.N. acknowledges funding from the European Union’s Horizon 2020 research andinnovation program under the Marie Sklodowska-Curie grant agreement No 898074.

Author contributions
N.K. conceived the idea and performed the experiments with the assistance of K.N., Y.T.,
and S.O.G.N., and M.G. fabricated the Si3N4 microresonators. N.K. wrote the manuscriptwith discussions and contributions from all the authors.

Competing interests
The authors declare no competing interests.

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