ARTICLE
Architecture for microcomb-based GHz-mid-
infrared dual-comb spectroscopy
Chengying Bao
1,3,5
, Zhiquan Yuan
1,5
, Lue Wu
1
, Myoung-Gyun Suh
1,4
, Heming Wang
1
, Qiang Lin
2
&
Kerry J. Vahala
1
✉
Dual-comb spectroscopy (DCS) offers high sensitivity and wide spectral coverage without
the need for bulky spectrometers or mechanical moving parts. And DCS in the mid-infrared
(mid-IR) is of keen interest because of inherently strong molecular spectroscopic signatures
in these bands. We report GHz-resolution mid-IR DCS of methane and ethane that is derived
from counter-propagating (CP) soliton microcombs in combination with interleaved differ-
ence frequency generation. Because all four combs required to generate the two mid-IR
combs rely upon stability derived from a single high-Q microcavity, the system architecture is
both simpli
fi
ed and does not require external frequency locking. Methane and ethane spectra
are measured over intervals as short as 0.5 ms, a time scale that can be further reduced using
a different CP soliton arrangement. Also, tuning of spectral resolution on demand is
demonstrated. Although at an early phase of development, the results are a step towards
mid-IR gas sensors with chip-based architectures for chemical threat detection, breath
analysis, combustion studies, and outdoor observation of trace gases.
https://doi.org/10.1038/s41467-021-26958-6
OPEN
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA.
2
Department of Electrical and Computer
Engineering, University of Rochester, Rochester, NY 14627, USA.
3
Present address: State Key Laboratory of Precision Measurement Technology and
Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China.
4
Present address: Physics & Informatics Laboratories, NTT
Research, Inc. 940 Stewart Dr, Sunnyvale, CA 94085, USA.
5
These authors contributed equally: Chengying Bao and Zhiquan Yuan.
✉
email:
vahala@caltech.edu
NATURE COMMUNICATIONS
| (2021) 12:6573 | https://doi.org/10.1038/s41467-021-26958-6 | www.nature.com/naturecommunications
1
1234567890():,;
D
ual-comb spectroscopy (DCS) works by mapping an
optical comb of frequencies into radio-frequencies by
multi-heterodyne beat with a second comb having a
slightly different repetition rate. Because the two combs sample
absorption spectra with a resolution set by their line spacing (or
repetition rate), analysis of the corresponding comb of radio
frequencies reveal these spectra in a multiplexed fashion without
the use of scanning gratings or interferometers
1
–
3
. Comb gen-
eration in the mid-infrared (mid-IR) has traditionally used
methods that rely upon mode-locked pulse generation, including
difference-frequency-generation (DFG), optical parametric oscil-
lation, and supercontinuum generation
3
,
4
; and there is con-
siderable progress using such systems for mid-IR DCS
5
–
14
. More
recently, mid-IR comb generation by DFG using electro-optic
frequency combs (EO-comb) has also been demonstrated
15
,
16
.In
contrast to conventional mode-locking, this approach offers rate
tunability to the X-band range (8
−
12 GHz) and higher
16
; and
because DCS systems can trade-off spectral resolution for higher
acquisition rates, such higher rates can be useful for the study of
dynamics
17
. With the advent of thin-
fi
lm lithium niobate tech-
nology, EO-combs have potential for chip-integration
18
. Indeed,
on-chip lithium niobate microcavity-based EO-combs have been
used for DCS in the near-IR
19
.
Also offering high repetition rates and chip integration are
soliton microcombs
20
,
21
. On account of their compact size, these
devices operate readily in the X to millimetre-wave bands.
Microcomb-based DCS has been reported at rates of 22 and 450
GHz in the near-IR
22
,
23
and 127 GHz in the mid-IR
5
. And while
offering extremely short acquisition times, these rates are too high
for spectroscopy of many species, leading to spectral under-
sampling of gas samples. For balance between acquisition rate
and spectral resolution, DCS at GHz rates is considered to be
relatively optimal for sensing of ambient gases (with linewidths
narrower than 10s of GHz)
24
–
26
. Special efforts have been
directed to reduce near-IR microcomb rates to the single-digit
GHz range
27
,
28
, but these require very high Q resonators to
reduce increased threshold pumping power associated with larger
mode volumes. Thermal tuning of large spacing microcombs has
also been used to improve the resolution for near-IR DCS at the
expense of measurement speed
29
. Aside from microcombs, an on-
chip III
−
V laser frequency comb with a line spacing of 1 GHz
(together with an EO-comb) has also been used for near-IR
DCS
30
. Nonetheless, mid-IR DCS with GHz resolution remains
quite challenging for chip-based devices, including quantum
cascaded laser frequency combs
31
,
32
.
Here, we report microcomb-based DCS with GHz resolution in
the mid-IR band. The two GHz-rate mid-IR combs are generated
by interleaved difference-frequency-generation (iDFG)
33
applied
to four near-IR combs. These four combs are linked to counter-
propagating (CP) solitons
34
formed within a single microcavity.
The frequency stability of the resulting mid-IR DCS spectra is
high on account of this simpli
fi
ed architecture in combination
with the high mutual coherence of the CP solitons. DCS mea-
surements of methane and ethane near 3.3
μ
m are performed.
Normalized precision as high as 1.0 ppm
⋅
m
ffiffi
s
p
is demonstrated.
Results
Architecture of the DCS system
. The experimental setup is
illustrated in Fig.
1
a. It shows two 3.3
μ
m frequency combs
generated in upper and lower branches of the optical train, fol-
lowed by combining (far right in the
fi
gure) for input to the test
gas cell. In accordance with the DCS procedure as described
elsewhere
2
the two combs are photodetected after passage
through the gas cell, and this multi-heterodyne process creates a
radio-frequency spectrum that contains the mid-IR absorption
spectrum of the gas. The spectrum is obtained by fast Fourier
transform (FFT) of the time-domain interferogram signal of the
dual combs. The gas cell (Wavelength Reference) has a length of
5 cm and contains ~2% methane (CH
4
) and ~0.5% ethane (C
2
H
6
)
buffered by nitrogen to a total pressure of 760 Torr (parameters
can have ±5% uncertainty). Such a methane concentration is
equivalent to about 1 ppm in an ambient environment when
passing the comb light through a 1 km open path for
fi
eld
measurements.
Each mid-IR comb is generated by iDFG in a PPLN crystal
(4 cm long, NTT Electronics) of two near-IR combs: a soliton
microcomb at 1.55
μ
m (Fig.
1
b) and an EO-comb (Fig.
1
c) at 1.06
μ
m. Counter-pumped clockwise (cw) and counter-clockwise
(ccw) solitons formed in a single silica resonator
35
are input to
upper and lower branches of the optical train. On account of the
silica Raman response, the soliton repetition rates (
f
cw
r
or
f
ccw
r
)
can be independently
fi
ne-controlled by two acousto-optical
modulators (AOMs) placed before the resonator
34
. Their
approximate repetition rate is 22 GHz. Another AOM after the
microcavity, driven by a
fi
xed 55 MHz signal, is used to shift the
frequencies of one of the microcombs so as to avoid spectral
aliasing upon multi-heterodyne beating of the two combs in both
the near-IR and the mid-IR. Each EO-comb drive frequency is
derived from a corresponding photo-detected soliton repetition
frequency and set to be
ð
N
1
Þ
f
cw(ccw)
r
=
N
(
N
is an integer).
This results in interleaving of the near-IR combs and densi
fi
es the
mid-IR comb line spacing to 22 GHz/
N
as described elsewhere
33
.
2.8 and 1.4 GHz mid-IR line spacings are demonstrated,
corresponding to
N
=
8 or 16.
For high precision measurements, the two mid-IR comb spectra
must have excellent relative frequency stability. Several features of
the current system architecture ensure this result while also
reducing the system complexity. First, the upper and lower optical
trains share common near-IR continuous-wave pumping lasers.
These pumps or their AOM-shifted replicas become comb lines in
each of the four near-IR combs. EO-combs, therefore, have identical
centre frequencies, while soliton combs have offset frequencies that
arerelatedbythedifferenceintheAOMfrequencyshifts(
Δ
ν
P
)
appliedtothesolitonpumps.Second,bytuningtherelative
counter-pumping frequency
Δ
ν
P
, the repetition rates of the two
microcombs (
f
cw
r
and
f
ccw
r
) become phase-locked such that
Δ
f
r
=
Δ
ν
P
/
M
(
Δ
f
r
¼
f
cw
r
f
ccw
r
and
M
is an integer)
34
. Because
the EO-comb rates are derived from the soliton comb rates, all four
combs, despite having different repetition rates, have their rates
phase-locked. This feature in combination with the common optical
pumps means that the two mid-IR combs have an offset frequency
noise equal to the
fl
uctuations in the difference frequency of the
1.55 and 1.06
μ
m pumps as their primary source of frequency
instability. Signi
fi
cantly, however, this is a common-mode
fl
uctua-
tion to the mid-IR combs and will therefore cancel out in the multi-
heterodyne DCS detection process. As a result, the frequency
stability of the mid-IR comb interferogram is extremely high, being
primarily determined by the relative stability of the two CP solitons.
This stability is accomplished without the need for frequency
locking procedures, because of the above-mentioned features of the
system architecture. Moreover, this architecture eliminates the need
for bulk microwave oscillators required for EO-combs.
To illustrate the frequency stability that is possible using this
architecture, a portion of the Fourier transform of the measured
dual-soliton interferogram (measured on a balanced receiver over
200 ms) is shown in Fig.
1
d. De
fi
ning the line-to-
fl
oor ratio (LFR)
as the square root of the ratio of signal power to the average noise
fl
oor power (see
“
Methods
”
), Fig.
1
e shows that the highest LFR
of the radio-frequency comb scales as 6.3
́
10
4
ffiffiffi
τ
p
=
ffiffi
s
p
(
τ
is the
measurement time). This value gives a measure of dynamic range
ARTICLE
NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-26958-6
2
NATURE COMMUNICATIONS
| (2021) 12:6573 | https://doi.org/10.1038/s41467-021-26958-6 | www.nature.com/naturecommunications
available for absorption measurement. The mutual stability of the
two microwave signals generated by photodetecting the soliton
streams was also tested by mixing
f
cw
r
and
f
ccw
r
. The measured
Allan deviation of their difference frequency
Δ
f
r
(Fig.
1
f) shows
that the two soliton microwave rates reach a relative frequency
fl
uctuation less than 1 Hz at around a millisecond of averaging
time. Then, the stability further improves to about 1 mHz at
100 s. This Allan deviation is found to be close to that of the
frequency
fl
uctuation of the AOM driver when setting its output
frequency close to
Δ
f
r
(see Fig.
1
f).
Characterization of the DCS system
. The transfer of mutual
coherence of the CP solitons to the mid-IR is veri
fi
ed in Fig.
2
a
where measured interferograms of the mid-IR combs are dis-
played. The mid-IR interferograms are collected by a fast pho-
todetector (600 MHz bandwidth, PVI-4TE-4, Vigo System SA),
and the optical power is around 60
μ
W (Supplementary Note 1)
to avoid detector nonlinearity. For comparison, interferograms
are shown using conventional DFG (EO-comb drives turned off
for soliton mixing with the 1.06
μ
m continuous-wave laser) as
well as iDFG with
N
=
8 and
N
=
16. In the DFG case, inter-
ferogram pulses repeat at the rate of
Δ
f
r
, while in the iDFG case
the pulses repeat at the rate of
Δ
f
r
/
N
. Note that even for the iDFG
case, there are pulses appearing at the rate
Δ
f
r
and it is the
envelope modulation of these pulses that re
fl
ect the interleaving
process. This non-ideal behaviour is mainly the result of three
effects that could be corrected in the future. First, the EO-comb
pulses themselves were not fully compressed (i.e., not tranform
limited), because of the lack of two dispersion control systems.
The dual-EO-comb interferogram suggests the extinction ratio of
the EO-pulses is about 8 dB. Second, based on the group
refractive index difference and length of the commercial PPLN
crystal, the temporal walk-off between two near-IR pulses is
estimated to be up to ~4 ps. Third, the PPLN phase-matching
bandwidth for this long crystal is quite narrow (<300 GHz) at
1.5
μ
m and leads to an effectively wider soliton pulse width.
A criterion for minimal residual pulses in iDFG can be given as,
t
s
þ
t
EO
þj
Δ
t
wkf
j
<T
s
=
N
;
ð
1
Þ
where
t
s
(
t
EO
) is the effective width of the soliton (EO) pulse,
Δ
t
wkf
is the walk-off between the near-IR pulses in the crystal, and
T
s
is the 1.55
μ
m soliton period. A detailed discussion of the
residual pulses is given in the Supplementary Note 4. The use of
fully compressed EO-combs in combination with a more optimal
PPLN would eliminate the residual RF pulses in the inter-
ferograms. In such an optimized arrangement only one RF pulse
would appear in the time period of
N
/
Δ
f
r
. This would also
eliminate spectral envelope modulation in the interferogram FFT
as noted below.
As an aside,
Δ
f
r
was tuned slightly in the measurements and, as
a result, the RF pulses are not aligned between the three cases in
Fig.
2
a. Furthermore, the PPLN temperature (and thus the phase-
matching condition) was also tuned in experiments so that the RF
1.55 μm cw
microcavity
EDFA
AOM
AOM
AOM
EDFA
1.06 μm cw
1/99
1/N
PM
IM
PPLN
WDM
EDFA
YDFA
PM
IM
YDFA
PPLN
WDM
1/99
1/N
50/50
Servo
10/90
circ.
circ.
Cell
Oscilloscope
a
50/50
10
-2
Time (s)
10
0
10
2
AOM driver
10
-4
10
-2
10
0
Allan
deviation
(Hz)
Frequency (MHz)
pump
80 kHz
b
Power (20 dB/div)
e
f
f
r
10
2
10
3
10
4
10
5
Peak LFR
10
-5
Linear fit
Data
10
-4
10
-3
10
-2
10
-1
10
0
f
r
cw
f
r
ccw
Power (20 dB/div)
Power (20 dB/div)
c
d
Wavelength (nm)
52
55
58
61
64
67
22.1 GHz soliton
19.3 GHz EO-comb
1062
1063
1064
1065
1510
1540
1570
1600
Fig. 1 Experimental setup of the GHz-mid-IR DCS system. a
Counter-propagating (CP) solitons at 1.55
μ
m are generated in a silica microcavity to provide
two of four comb signals. These solitons are photo-detected and the resulting signals are processed to create the two other comb signals by electro-op
tic
modulation at 1.06
μ
m. These near-IR combs are combined in pairs to pump PPLN crystals for generation of GHz line spacing mid-IR combs by interleaved
difference frequency generation. These mid-IR comb sources pass through a gas cell and are detected for dual-comb spectroscopy. Fiber Bragg grating
fi
lters used to
fi
lter pump waves in the soliton microcomb spectra are omitted in the
fi
gure.
f
cw
r
(
f
ccw
r
) corresponds to the cw (ccw) soliton repetition
rates. AOM: acousto-optical modulator, circ: circulator, PM: phase modulator, IM: intensity modulator, EDFA: erbium-doped
fi
bre ampli
fi
er, YDFA:
ytterbium-doped
fi
bre ampli
fi
er, WDM: wavelength division multiplexer, PPLN: periodically poled Lithium Niobate. Scale bar: 1 mm.
b
Optical spectrum of
1.55
μ
m soliton comb.
c
Optical spectrum of 1.06
μ
m EO-comb.
d
Multi-heterodyne beat between two CP soliton microcombs (repetition rate difference,
Δ
f
r
, is 80 kHz). The beat note produced by the counter-pumps is identi
fi
ed. One of the microcombs is shifted by 55 MHz using the AOM placed after the
cavity (see diagram in panel
a
).
e
Peak LFR of the comb lines in panel (
d
) as a function of averaging time
τ
. The solid line is a
fi
t of the
ffiffiffi
τ
p
trend.
f
Measured
Allan deviation of
Δ
f
r
is close to the stability of the AOM driver. The frequency of the AOM driver (a radio frequency function generator) was set to be
Δ
f
r
in this measurement. The error bar corresponds to the standard deviation of the Allan deviation.
NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-26958-6
ARTICLE
NATURE COMMUNICATIONS
| (2021) 12:6573 | https://doi.org/10.1038/s41467-021-26958-6 | www.nature.com/naturecommunications
3
pulses exhibit different envelope modulation for the iDFG
N
=
8
and
N
=
16 cases.
FFT of the interferograms yields the radio-frequency combs
shown in Fig.
2
b. Digital correction described in the
“
Methods
”
was used here to compensate
fl
uctuations induced by
fi
bres
connecting comb generation and gas cell spectroscopy setups,
which resided in different laboratories (see discussion relating to
Fig.
2
e in Supplementary Note 2). Co-location of the setups to a
single table (or ultimately integration of the components) should
avoid this
fl
uctuation and simplify data processing. In the spectra,
the conventional DFG case has a line spacing of
Δ
f
r
, while the
iDFG cases have a line spacing narrowed to
Δ
f
r
/
N
. Spectral
envelope modulation appearing for
N
=
8 and
N
=
16 (compare
to conventional DFG spectrum) results from the non-ideal
residual pulses discussed in Fig.
2
a. A zoom-in of the RF comb
spectra in Fig.
2
c shows the densi
fi
cation of the lines.
As noted above, the full optical microcomb bandwidth was not
available for mid-IR comb generation due to the limited phase-
matching bandwidth of the PPLN crystals. This limitation can be
observed in the DFG interferogram spectrum in Fig.
2
b, where
the comb line intensity decreases rapidly from the spectrum
centre. To somewhat reduce this limitation in the current
measurements, the temperature of the two PPLN crystals was
set to be slightly different so as to enlarge the usable bandwidth in
the mid-IR.
To measure the absolute frequency stability of the dual-comb
interferogram spectra, the Allan deviation of a single multi-
heterodyne beat frequency is calculated in Fig.
2
d for mid-IR, CP
and EO generated spectra. Using conventional DFG the
frequency stability is comparable to that of the near-IR CP
solitons. Here, the stability is better than 1 Hz within 100 ms
averaging time as a result of stability linked to the single
microcavity. A slight degradation is observed for the iDFG
N
=
8
and iDFG
N
=
16 cases, which may result from additional noise
contributed by the EO-combs. This is substantiated in Fig.
2
dby
Allan deviation measurement of a single frequency within a
DFG
iDFG
N
=8
iDFG
N
=16
1/Δ
f
r
8/Δ
f
r
1/Δ
f
r
16/Δ
f
r
1/Δ
f
r
Time (50 μs/div)
Voltage (
0.5 V/div)
b
DFG
45
55
47
49
51
53
47
52
48
49
50
51
52
48
49
50
51
iDFG
N
=8
iDFG
N
=16
Frequency (MHz)
49.64
49.72
50.11
50.17
Frequency (MHz)
Power (20 dB/div)
Power (20 dB/div)
Power (20 dB/div)
Powe
r (20 d
B
/div)
Powe
r
(20 d
B/div)
Power
(20 dB/div)
c
e
Peak LFR
10
-
²
10
-
³
10
-
⁴10
-
¹
f
f
(mid-IR 22 GHz)
r
f
(mid-IR 22 GHz)
r
f
(mid-IR 22 GHz)
r
10
-3
10
-2
10
-1
d
a
49.46
49.53
10
-1
10
0
10
1
Adev. of comb line freq. (Hz)
Sum-SNR
Average SNR
Soliton
EO-comb
DFG
iDFG
N
=8
iDFG
N
=16
2.0e4 s
-1/2
6.8e3 s
-1/2
4.0e3 s
-1/2
iDFG
N
=8 (w/o corr.)
DFG
iDFG
N
=8
iDFG
N
=16
Linear fit
10
2
10
3
10
4
10
5
10
3
10
4
10
2
10
0
10
1
10
-4
Time (s)
10
-3
10
-2
10
-1
DFG
iDFG
N
=8
iDFG
N
=16
Ref. 7
Ref. 8
Ref. 12
Ref. 7
Ref. 12
Fig. 2 Interferograms and multi-heterodyne spectra of the iDFG densi
fi
ed mid-IR combs. a
Interferogram of the mid-IR combs using DFG and iDFG. The
interferograms for the iDFG combs repeat at a rate of
Δ
f
r
/
N
.
b
Dual-comb spectra formed by fast Fourier transform of the measured interferograms. The
radio frequency combs are spectrally densi
fi
ed when using iDFG.
c
Zoom-in of the radio-frequency combs in panel (
b
). A 22 GHz scale giving the
corresponding optical bandwidth in the mid-IR is provided.
d
Allan deviation of the frequency of a single line measured at the centre of the multi-
heterodyne spectra plotted versus the measurement time. The generation mechanism is indicated in the legend. The error bar corresponds to the standa
rd
deviation of the Allan deviation.
e
Plot of the LFR versus measurement time
τ
for strongest spectral line using conventional and interleaved DFG. The solid
lines are linear
fi
ts (
ffiffiffi
τ
p
trend in the log
−
log plot). All circular points are digitally corrected. Squares points show the uncorrected results for
N
=
8.
f
Plot of
the sum- and average SNR of our mid-IR DCS system versus the measurement time
τ
. Black dashed lines are SNR for reported mid-IR DCS systems.
ARTICLE
NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-26958-6
4
NATURE COMMUNICATIONS
| (2021) 12:6573 | https://doi.org/10.1038/s41467-021-26958-6 | www.nature.com/naturecommunications
multi-heterodyne spectrum produced using only two 1.06
μ
m
EO combs.
To further con
fi
rm the mutual phase coherence in the mid-IR,
the LFR of the mid-IR interferogram spectra (calculated using the
strongest spectral peak) is analyzed in Fig.
2
e. In all three cases
(DFG, iDFG
N
=
8, and iDFG
N
=
16), the LFR shows a
ffiffiffi
τ
p
trend (after digital correction), and scales as 2.0
́
10
4
ffiffiffi
τ
p
=
ffiffi
s
p
,
6.8
́
10
3
ffiffiffi
τ
p
=
ffiffi
s
p
, and 4.0
́
10
3
ffiffiffi
τ
p
=
ffiffi
s
p
, respectively. Data obtained
without digital correction (squares) for iDFG
N
=
8 are also
presented and show that the mutual coherence is preserved up to
10 ms until the aforementioned
fi
bre
fl
uctuations cause
deterioration (see Supplementary Note 2). The high LFR can
enable high dynamic range spectroscopic measurements.
To further characterize the DCS system, the signal-to-noise
ratio (SNR: square root of the ratio of the signal to the standard-
deviation of the
fl
uctuations)
2
,
7
–
9
,
15
of lines in the FFT of the
interferogram is calculated (see
“
Methods
”
). These values are then
used to compute the sum-SNR (upper panel of Fig.
2
f) and
average SNR (lower panel of Fig.
2
f) versus integration time over
lines within 40 dB of the strongest line
2
. The sum-SNR initially
increases as
ffiffiffi
τ
p
within 2 ms, but then saturates at longer
averaging times. For comparison, the sum-SNRs for other
reported mid-IR DCS systems are plotted as dashed lines.
Considering the good frequency stability of the present system,
the relatively low sum-SNR is likely limited by the amplitude
noise of the mid-IR combs. It is possible that this could result
from the use of
fi
bre-taper optical coupling to the resonator,
which can introduce a mechanism for environmental noise to
impact coupling. The use of a fully integrated microcomb would
avoid this problem. Moreover, the use of a reference mid-IR
photodetector would enable monitoring of power
fl
uctuations
22
and could help to boost the sum-SNR. Although the sum-SNR is
relatively low, the average SNR of the spectrum is relatively high
and enables a fast measurement. This results from fewer usable
lines in the current system compared with the
fi
bre-based mid-IR
systems.
Mid-IR DCS of methane and ethane
. The mid-IR DCS system
was used to measure the absorbance spectra of a mixture of
methane and ethane gas. The dual-comb spectrum with the gas
cell inserted (
T
) was
fi
rst measured and then normalized by the
reference spectrum measured without the gas cell (
T
0
). The
absorbance is then calculated as
ln
ð
T
=
T
0
Þ
. The wavelength of
the 1.06
μ
m laser (an external cavity diode laser) was tuned to
access rovibrational transitions belonging to different branches in
the
ν
3
band of methane
36
. The
Q
-branch of methane around 3015
cm
−
1
was
fi
rst measured. The absorbance spectra measured by
DFG and iDFG
N
=
8 DCS are presented in Fig.
3
a. We compare
the measured spectra to the HITRAN database using the gas cell
information given above (the absolute frequency offset was used
as a free parameter for the best
fi
t). While both absorbance
spectra are in a good agreement with the HITRAN database
37
the DFG spectrum undersamples the methane spectral features
due to its relatively wide 22 GHz comb line spacing, and only
three data points (green points) appear for the zoom-in spectrum
in Fig.
3
a. On the other hand, this spectral undersampling is
avoided by using iDFG DCS with a reduced comb line spacing of
2.8 GHz corresponding to iDFG with
N
=
8. The residuals
between the measured spectrum and HITRAN database are
plotted in the lower panel. The non-negligible residuals re
fl
ect the
relatively low sum-SNR shown in Fig.
2
f. Additional data
obtained for the
P
-branch of methane (e.g.,
P
(3),
P
(6), and
P
(7))
are presented in Fig.
3
b, c. The measured spectra are also in good
agreement with the HITRAN database. The ethane absorption
spectrum in the
ν
7
band
38
was also measured in Fig.
3
c. Such an
ability to measure the methane and ethane simultaneously is
important to distinguish if the methane emission comes from gas
wells
39
.
A feature of iDFG DCS is that the spectral resolution can be
adjusted by changing the division ratio
N
33
. For instance, the full-
width at half-maximum (FWHM) of methane
P
(3) to
P
(7)
transition groups in the
ν
3
band are within 10
−
26 GHz, while the
FWHM of ethane
P
Q
1
to
P
Q
4
transitions in the
ν
7
band are within
4.2
−
6.9 GHz according to the HITRAN database. Improved
resolution of the ethane absorbance via iDFG DCS is shown as
the red dots in Fig.
3
c. Here, a
fi
ner resolution of 1.4 GHz is
achieved by selecting
N
=
16. In principle, the resolution of the
DCS system could be adjusted in steps from GHz to 22 GHz,
making it possible to optimize resolution and SNR depending
upon the characteristics of the gas sample.
The GHz DCS system also enabled fast and precise measure-
ment of the absorbance spectrum. Measurement precision is
evaluated using the Allan deviation of the measured methane
concentration in the 5 cm cell. 200 ms interferograms were
separated into 400 slots and the methane concentration was
calculated in each resulting 0.5 ms slot (corresponding to about 5
interferogram periods for iDFG
N
=
8). Figure
3
d details the
evaluation process for the
P
(3) branch measurement with iDFG
N
=
8. The top panels are representative spectra from two 0.5 ms
time slots (numbers 100 and 300) without any digital correction
as mutual coherence is preserved. They illustrate fast acquisition
of the methane absorption spectrum, which can result from the
relative high average SNR achieved in short time. Fitting each
absorbance spectrum to the HITRAN database yields the
measured methane concentration in each time slot (lower panel
of Fig.
3
d). Since about 20~30 comb lines in the absorption
spectra are used to
fi
t for the concentration, the residuals between
the observation and HITRAN are found to not signi
fi
cantly
degrade the measurement precision. This measured concentration
sequence was then used to calculate the Allan deviation of the
measured methane concentration, which was further normalized
by the gas cell length to derive the normalized measurement
precision in Fig.
3
e (all for the iDFG
N
=
8 case). The Allan
deviation (
P
(3) branch measurement) reaches a precision of ~2.8
ppm
⋅
m within 64 ms. In
fi
tting the Allan deviation of the
P
(3)
branch measurement to a 1
=
ffiffiffi
τ
p
trend line, a normalized
measurement precision of 1.0 ppm
⋅
m
ffiffi
s
p
can be obtained.
Measurements of rovibrational transitions in other branches
produce similar results. This sub-ms measurement time may
make this system suitable for studies of transient events in
combustion
17
.
The measurement acquisition times of 200 ms for Fig.
3
a, c and
100 ms for Fig.
3
b are shorter than
fi
bre-comb-based mid-IR DCS
systems, which generally require an acquisition time longer than
tens of seconds
8
,
11
,
12
(usually those systems have a much larger
comb line number). Even shorter acquisition times should be
possible that are comparable to EO-comb-based systems, where
mid-IR DCS has also been demonstrated
15
. To attain a shorter
acquisition time, CP solitons with a larger
Δ
f
r
generated on
distinct mode families could be utilized
40
.
Discussion
In this work, microcomb-based DCS in the mid-IR with GHz
resolution has been demonstrated. This represents a 100-fold
improvement in spectral resolution compared with previous mid-
IR microcomb DCS. Mutual coherence of near-IR CP solitons
enables precise methane absorption measurements reaching a
normalized precision of 1.0 ppm
⋅
m
ffiffi
s
p
. While the demonstrated
system still relies upon
fi
bre optics, further integration of the
system on a photonic chip is feasible. Along this direction, both
NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-26958-6
ARTICLE
NATURE COMMUNICATIONS
| (2021) 12:6573 | https://doi.org/10.1038/s41467-021-26958-6 | www.nature.com/naturecommunications
5