# Frequency-scanned microresonator soliton comb with the tracking of the
frequency of all comb modes

Naoya Kuse  Institute of Post-LED Photonics, Tokushima University, 2-1,
Minami-Josanjima, Tokushima, Tokushima 770-8506, Japan  PRESTO, Japan Science
and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
Corresponding author<EMAIL_ADDRESS>Gabriele Navickaite
LIGENTEC SA, EPFL Innovation Park L, Chemin de la Dent-d’Oche 1B, Switzerland
CH-1024 Ecublens, Switzerland  Michael Geiselmann  LIGENTEC SA, EPFL
Innovation Park L, Chemin de la Dent-d’Oche 1B, Switzerland CH-1024 Ecublens,
Switzerland  Takeshi Yasui  Institute of Post-LED Photonics, Tokushima
University, 2-1, Minami-Josanjima, Tokushima, Tokushima 770-8506, Japan
Graduate School of Technology, Industrial and Social Sciences, Tokushima
University, 2-1, Minami-Josanjima, Tokushima, Tokushima 770-8506, Japan  Kaoru
Minoshima  Institute of Post-LED Photonics, Tokushima University, 2-1, Minami-
Josanjima, Tokushima, Tokushima 770-8506, Japan  Graduate School of
Informatics and Engineering, The University of Electro-Communications, 1-5-1
Chofugaoka, Chofu, Tokyo 182-8585, Japan

###### Abstract

Rapid and large scanning of a dissipative Kerr-microresonator soliton comb
with the characterization of all comb modes along with the separation of the
comb modes is imperative for the emerging applications of the frequency-
scanned soliton combs. However, the scan speed is limited by the gain of
feedback systems and the measurement of the frequency shift of all comb modes
has not been demonstrated. To overcome the limitation of the feedback, we
incorporate the feedback with the feedforward. With the additional gain of >
40 dB by a feedforward signal, a dissipative Kerr-microresonator soliton comb
is scanned by 70 GHz in 500 $\mu$s, 50 GHz in 125 $\mu$s, and 25 GHz in 50
$\mu$s (= 500 THz/s). Furthermore, we propose and demonstrate a method to
measure the frequency shift of all comb modes, in which an imbalanced Mach-
Zehnder interferometer with two outputs with different wavelengths is used.
Because of the two degrees of freedom of optical frequency combs, the
measurement at the two different wavelengths enables the estimation of the
frequency shift of all comb modes.

††journal: ol

Dissipative Kerr-microresonator soliton combs (hereafter called soliton combs)
have been generated from CMOS compatible platforms, providing the potential to
be fully integrated optical frequency combs [1, 2]. After various
demonstrations such as ultra-fast ranging [3, 4], optical frequency
synthesizers [5], dual-comb spectroscopy [6, 7], and low phase noise microwave
generation [8, 9] using free-running or frequency-stabilized soliton combs,
recently, frequency-scanned soliton comb explores new type of applications.
One distinguished example is ultra-fast frequency-modulated continuous-wave
(FMCW) LiDAR [10], in which a frequency-scanned soliton comb is used as a set
of massive parallel frequency-scanned cw lasers. Another example is scanning
soliton comb spectroscopy [11, 12, 13]. The frequency-scanned soliton comb
overcomes the sparsity of the soliton comb, which limits the frequency
resolution for spectroscopy. To fully open up the potential of the frequency
scanned soliton comb such as high-speed and precise measurements, two
fundamentals have to be developed, that is (1) rapid and large scanning and
(2) measurement of the frequency shift of all comb modes.

When soliton combs are scanned, both the frequencies of a pump cw laser and a
resonance of a microresonator have to be scanned simultaneously to keep the
detuning between the pump cw laser and the resonance in a range where soliton
combs are maintained. Conventionally, the detuning is fixed by employing a
feedback loop based on Pound-Drever-Hall (PDH) locking [12, 14] or soliton-
power locking [15, 13]. In ref [12] and ref [13], the comb mode scanning of
190 GHz (scan speed is not shown) and 31 GHz in 50 ms (= 0.62 THz/s) has been
demonstrated, respectively. However, in the methods with feedback loops, the
scan speed is limited by the feedback gain and dynamic range of a modulator
(e.g. pump cw laser in ref [12, 13]) at the modulation frequency. On the other
hand, the feedforward scheme, where the frequencies of a pump cw laser and
resonance are controlled by a pre-determined signal, is free from the feedback
gain limit [16]. However, due to the non-fixed detuning, a large range
scanning is very difficult without sophisticated feedforward signals.
Regarding the frequency measurement, none has demonstrated the measurement of
all comb modes. When a soliton comb is used for massively parallel FMCW LiDAR
[10], the frequency of the soliton comb is partially measured by measuring the
frequency of a beatnote between one of the comb modes and a cw laser. In ref
[12], where comb-resolved high-resolution spectroscopy has been demonstrated,
the frequency of only one comb mode used for spectroscopy is measured by using
an imbalanced Mach-Zehnder interferometer (i-MZI). In these cases, the full
characterization of all comb modes cannot be achieved.

In this letter, we demonstrate the rapid and large scanning of a soliton comb
with the measurement of the frequency shift of all comb modes, showing the
frequency scanning of 25 GHz in 50 $\mu$s (= 500 THz/s) with the estimated
frequency error of below 10 MHz. The rapid and large scanning of the comb mode
is enabled by incorporating the feedback with the feedforward. In addition to
the feedback gain of 40 dB, the feedforward signal provides 40 dB gain when
the modulation frequency of 10 kHz is applied to a microheater. Because of the
large gain at the modulation frequency, the comb modes are successfully
scanned by 25 GHz in 50 $\mu$s (70 GHz in 500 $\mu$s, 50 GHz in 125 $\mu$s
when modulation frequencies of 1 kHz and 4 kHz are applied), which is limited
by the used microheater. For the tracking of the frequency shift of all comb
modes, we propose a two-wavelength i-MZI, in which the frequency shifts of the
two of the comb modes are tracked. Since the frequencies of the comb modes are
highly correlated as expressed with the only two degrees of freedom ($f_{\rm
ceo}$: carrier-envelope offset frequency and $f_{\rm rep}$: comb mode
spacing), the frequency shift of all comb modes can be estimated from the
measurement of the two comb modes.

Figure 1: Illustrations of an error signal in the time domain (a) and
frequency domain (b). (c) Schematic of the experimental setup. (d) The optical
spectrum of the soliton comb. (e) The frequency response of the microheater
when 10 mW electric power is applied. The dotted curve is a Lorentz function.

The basic concept of our scan system is illustrated in Figs. 1 (a) and (b). In
our scan system with feedback and feedforward, a microheater deposited on a
microresonator [12] is modulated by a pre-determined signal, which could be
arbitrary (e.g. $A{\rm sin}(f_{m}t)$ in the demonstration, where $A$, $f_{m}$,
and $t$ are modulation amplitude, modulation frequency, and time,
respectively). In the time domain, an error signal is considered as the sum of
a sine function and a random noise. In the frequency domain, a power spectral
density (PSD) of the error signal is expressed as the sum of a single tone at
$f_{m}$ and broadband noise. The sine function/single tone noise is generated
from a control signal applied to the microheater. The random/broadband noise
is originated from the noise of the pump cw laser and microresonator. The sine
function (single tone) in the time domain (in the frequency domain) is
suppressed by a feedforward signal, while the random (broadband) noise is
suppressed by a feedback signal.

An experimental setup is shown in Fig. 1 (c) (more detail is shown in the
supplementary material). A microresonator based on Si3N4 (SiN, width = 2
$\mu$m and height = 800 nm) is used for the generation of a single soliton
comb. The free spectral range (FSR) and loaded Q of the microresonator are
about 192 GHz and $10^{6}$, respectively. A distributed feedback (DFB) laser
around 1548 nm (AA1406 series from G&H) is directed through a phase modulator
(MPZ-LN-10 from iXblue), which is driven by an RF oscillator with the
modulation frequency ($f_{\rm PDH}$). $f_{\rm PDH}$ determines the detuning
between the DFB laser and the resonance frequency. The generated soliton comb
is guided to a two-wavelength i-MZI to characterize the frequency shift of all
comb modes. The details are explained later. The residual pump is
photodetected to generate an error signal for PDH locking. When the frequency
of the upper sideband that is generated from the phase modulator crosses the
resonance frequency, the error signal, which is generated after demodulation
by a double balanced mixer, has a zero-crossing voltage [12]. A feedforward
(FF) signal is added to the feedback (FB) signal, making a ‘feedforward-
feedback (FF-FB)’ signal. The feedforward-feedback (FF-FB) signal is then
applied to the DFB laser. The optical spectrum of the single soliton comb used
in the experiments is shown in Fig. 1(d). The comb mode spacing corresponds to
the FSR of the microresonator. Figure 1(e) shows the response of the
microheater when about 10 mW electric power is applied. The 3 dB modulation
bandwidth of the microheater is about 7 kHz.

Figure 2: (a) PSD of the error signal for the free-running (blue) and locked
(red) cases. The color map indicates how stable the detuning (i.e. soliton)
is. See the definition in the main text. The green and red circles are the
PSDs of the error signals at the modulation frequency when the DFB laser is
modulated by 35 MHz for the green circle and 230 MHz for the red circle with
the modulation frequency of 10 kHz, which corresponds to the error signal in
the time domain (b) for the green circle and (c) for the red circle.

The blue curve in Fig. 2(a) shows the power spectral density (PSD) of the
error signal when the detuning is slowly (< 100 Hz feedback bandwidth) locked
at 1100 MHz, which is the middle of the soliton-existing detuning (from 800
MHz to 1400 MHz), by the feedback loop without any FF signal. In Fig. 2(a), we
distinguish the power of the single tone noise ($P_{\rm tone}$) against the
soliton-existing detuning range ($\Delta_{\rm sol}$); blue, green, and red
zones are termed as ‘quiet’ ($P_{\rm tone}$ < 5 % of $\Delta_{\rm sol}$),
‘safe’ (5 % of $\Delta_{\rm sol}$ < $P_{\rm tone}$ < 33 % of $\Delta_{\rm
sol}$), and ‘fragile’ (33 % of $\Delta_{\rm sol}$ < $P_{\rm tone}$) in this
letter, respectively. In the ‘fragile’ zone, the soliton comb can be lost.
When a tiny 10 kHz modulation is added to the DFB laser in addition to the
slow feedback signal, the error signal in the time domain shows the
oscillation at 10 kHz (Fig. 2(b)). The excursion of the error signal is 35
MHz, which corresponds to the green circle in the frequency domain in Fig.
2(a). The applied tiny single tone brings the error signal from ‘quiet’ to
‘safe’. When a larger 10 kHz modulation is added to the DFB laser, the error
signal shows the nonlinear behavior due to the deviation from the linear range
of the PDH locking (Fig. 2(c)). Assuming a linear response of the error
signal, the excursion of the error signal is 230 MHz, which corresponds to the
red circle in the ‘fragile’ zone in Fig. 2(a). When a feedback loop with a
large locking bandwidth (> 100 kHz) is applied, the PSD of the error signal is
significantly suppressed as shown in the red curve in Fig. 2(a). At the 10 kHz
frequency offset, the feedback gain is more than 40 dB, which can bring both
green and red circles into the ‘quiet’ zone. However, when the microheater is
modulated by more than 25 GHz at 10 kHz, which is even 40 dB higher than the
red circle, the feedback loop cannot even bring the PSD back to the ‘safe’
zone. Therefore, the only feedback signal is not enough for rapid and large
comb mode scanning.

To overcome the limitations of the feedback-only system, the FF signal is
added to the FB signal, generating an FF-FB signal. A procedure to make the
FF-FB is described in the supplementary material. Figure 3(a) shows an error
signal when the microheater is modulated by about 2.3 GHz at 10 kHz. Because
of the limited feedback gain, the error signal shows an oscillation (the blue
curve in Fig. 3(a)), being in the ‘safe’ zone for the PSD of the error signal.
When a feedforward is turned on, the oscillation is suppressed as shown in the
red curve in Fig. 3(a). The PSD of the error signal at 10 kHz frequency offset
is suppressed by more than 40 dB as shown in Fig. 3(b), being brought into the
‘quiet’ zone. In total, our control system has more than as large as 80 dB (40
dB by feedback and 40 dB by feedforward) gain at 10 kHz, which is large enough
to reach the limit of the scan range of the microheater.

Figure 3: (a) Error signals with only feedback (blue curve) or both feedback
and feedforward (red curve) when the microheater is modulated by 2.3 GHz at 10
kHz. (b) PSD of the error signal, which corresponds to (a).

With the proposed control system, the comb modes are scanned rapidly and
largely. In the demonstration, the modulation frequencies of 1 kHz, 4 kHz, and
10 kHz with about 170 mW electric power are applied to the microheater.
Although more electric power could be applied, we have not tried such high
electric power not to break the microheater through electromigration. The
frequency of the DFB laser during the comb mode scanning is measured by an
i-MZI as shown in Fig. 4. The frequency shift is about 70 GHz, 52 GHz, and 26
GHz for 1 kHz (green curve in Fig. 4), 4 kHz (blue curve in Fig. 4), and 10
kHz (red curve in Fig. 4) modulation frequencies, which corresponds to the
scan speed of more than 550 THz/s at the fastest. In the fastest case, the
demonstrated scan speed is 1000 times faster than the previous demonstration
[13]. The scan range could be further improved by overcoming the scan range of
our microheater, because the DFB laser can be also scanned more than 80 GHz at
10 kHz. A new microheater has a scan range of 210 GHz, 180 GHz, and 120 GHz at
1 kHz, 4 kHz, and 10 kHz, respectively (more data is shown in the
supplementary material), although a single soliton comb cannot be generated
due to a failure of the design of microresonators. 80 dB gain of the proposed
method is large enough for the scanning of 80 GHz at 10 kHz, which is the
limit of the DFB laser, to be in the ‘safe’ zone in the PSD of the error
signal. To cover one FSR of soliton combs, microresonators with smaller FSR
would be required.

Figure 4: Frequency shift of a comb mode at 1 kHz (green), 4 kHz (blue), and
10 kHz (red) when the electric power of 170 mW is applied to the microheater.

The frequency shifts show the nonlinearity (close to a sine function in our
experiment), which causes the degradation of the depth resolution and
precision of LiDAR with the frequency-scanned soliton comb. Also, the
frequency shifts should be precisely characterized when the frequency-scanned
soliton comb is applied to spectroscopy. Therefore, a method to measure the
frequency shift of all comb modes is proposed. Once the frequency shift of all
comb modes is measured, the nonlinearity is corrected by signal processing
[17]. The system consists of a two-wavelength i-MZI (the time delay between
two arms is 1.35 ns) (Fig. 5(a)). Two outputs from the i-MZI are optically
bandpass filtered to extract a single comb mode at different frequencies (e.g.
$\nu_{m}$ and $\nu_{n}$), followed by photodetectors. The frequency shift of
the m-th and n-th ($\delta_{m}$ and $\delta_{n}$) comb modes is estimated from
the phase of the photodetected signals, which are expressed by using the
frequency shift of the comb mode spacing and the carrier-envelope offset
frequency ($\delta_{\rm rep}$ and $\delta_{\rm ceo}$) as

$\delta_{m(n)}=m(n)\delta_{\rm rep}+\delta_{\rm ceo}.$ (1)

With the measurement of $\delta_{m}$ and $\delta_{n}$, the frequency shift of
the k-th comb mode ($\delta_{k}$, k is an arbitrary integer) can be estimated
because the comb modes have only two degrees of freedom (i.e. $f_{\rm rep}$
and $f_{\rm ceo}$).

$\delta_{k}=\delta_{n}+\frac{k-n}{n-m}\cdot\left(\delta_{n}-\delta_{m}\right).$
(2)

Figure 5(b) shows the frequency shift of the -12th (red curve in Fig. 5(b))
and +12th (blue curve in Fig. 5(b)) comb modes. The amount of the frequency
shift between the two comb modes is different, indicating the comb mode
spacing is changed when the microheater is used for the scan. $\delta_{\rm
rep}$ can be also estimated from the measurement as

$\delta_{\rm rep}=\frac{\delta_{m}-\delta_{n}}{m-n}.$ (3)

The estimated $\delta_{\rm rep}$ is compared with the measurement, in which
the frequency of a beatnote between the electro-optically generated sidebands
from the neighboring comb modes is counted [18] (more detail is shown in the
supplementary material) by an RF spectrum analyzer. As shown in Fig. 5 (c),
the two independent measurements of $\delta_{\rm rep}$ are well overlapped.
Due to the limited data acquisition time of the used RF spectrum analyzer, the
scan speed is 0.5 Hz in these measurements. To investigate the precision of
the proposed measurement, another output is added to the i-MZI. The output
with another optical bandpass filter and photodetector is used to measure the
frequency shift of the -6th comb mode. The measured frequency shift of the
-6th comb mode is compared with that estimated from the -12th and +12th comb
modes. As shown in Fig. 5(d), The frequency difference between the measurement
and the estimation is about 10 MHz over the frequency shift of 50 GHz. As
shown in the supplementary material, even when the frequency shift of the same
comb mode is measured, the estimated frequency shift shows a similar frequency
error, which indicates the frequency error does not depend on the integer k as
long as the k-th comb mode is between the m-th and n-th comb mode. On the
contrary, when the integer k is outside of the measured two comb modes, the
frequency error scales up with the factor of $\frac{k-n}{n-m}$. Also, when the
same measurement is implemented without the soliton comb, the frequency error
is smaller. Therefore, the frequency error is likely to be caused by the
slowly-varying amplitude noise of the photodetected signal, inducing the phase
error in our signal processing. The frequency error might be reduced by using
an optical 90-degree hybrid coupler and balanced photodetection.

Figure 5: (a) Schematic of the two-wavelength i-MZI. (b) Frequency shift of
the +12th (blue) and -12th (red) comb modes. (c) $f_{\rm rep}$ shift measured
by the EO sideband method (dashed blue) and the two-wavelength i-MZI (red).
(d) Frequency error of the two-wavelength i-MZI estimated from (b).

In the demonstration, although the only frequency shift is measured, the
absolute frequency of all comb modes can be also estimated by referencing two
known frequencies such as molecular absorption lines or two reference cw
lasers whose absolute frequencies are known (more information in the
supplementary material). To minimize the i-MZI, the fiber-based i-MZI can be
replaced by optical waveguides on a chip, including optical couplers, delay,
arrayed-waveguide gratings (or microrings) for optical bandpass filtering, and
photodetectors.

To summarize, we have developed the two fundamental techniques for the
scanning of the soliton comb; (1) rapid and large scanning of the comb modes,
and (2) measurement of the frequency shift of all comb modes. By successfully
incorporating the feedback with the feedforward, a control gain beyond the
feedback system has been obtained. With the proposed control method with 80 dB
gain (more than 40 dB each from the feedback and feedforward) at the 10 kHz
frequency offset, the comb mode scanning of 26 GHz at 10 kHz (70 GHz for 1
kHz, 52 GHz for 4 kHz) limited by the used microheater was obtained, which is
equal to the scan speed of 550 THz/s. Also, the two-wavelength i-MZI has been
proposed and demonstrated to measure the frequency shift of all comb modes of
the soliton comb. The estimated frequency error was below 10 MHz over 50 GHz
comb mode scanning. Given that 100 comb modes with the comb mode spacing of 50
GHz are scanned by 50 GHz at a 10 kHz rate, the soliton comb can cover 5 THz
in 50 $\mu s$, which corresponds to a cw laser with the scan range and speed
of 5 THz and 100 PHz/s, respectively. Therefore, the rapidly and largely
scanned soliton comb in conjunction with a WDM system extremely accelerates
the spectroscopic system using a frequency-scanned cw laser. Not only to
replace the frequency-scanned cw laser, but the demonstrated frequency-scanned
soliton comb could be readily applied to FMcomb LiDAR [12], high-resolution
optical vector analyzer [19], and comb-resolved dense imaging [20, 21] in
addition to higher-depth resolution massively parallel FMCW LIDAR [10] and
faster comb-resolved spectroscopy [12].

Funding. This work was financially supported by JST PRESTO (JPMJPR1905),
Research Foundation for Opto-Science and Technology, KDDI Foundation, and
Cabinet Office, Government of Japan (Subsidy for Reg. Univ. and Reg. Ind.
Creation).

Disclosures. The authors declare no conflicts of interest.

Supplemental document See Supplement 1 for supporting content.

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