Introduction

Time-domain monitoring of fast chemical reactions is of particular interest in several fundamental and applied scientific fields, including physical chemistry, plasma/combustion analysis, biology, and atmospheric studies1,2,3,4. Broadband, time-resolved absorption spectroscopy can provide the possibility to simultaneously monitor time-dependent parameters of the chemical reactions, such as concentrations of intermediate/final chemical products, transient free radicals and ions, as well as branching ratios, reaction rate coefficients, temperature and number densities of molecular excited-states. Generally, the main challenge is to obtain a broadband spectrum with high spectral resolution and high detection sensitivity in a short measurement time. Continuous-wave (cw) laser absorption spectroscopy can provide time-resolved measurements for a single chemical species with a high detection sensitivity. However, for a broad spectral coverage the laser source needs to be scanned over the spectral range, inevitably reducing the measurement speed. Alternatively, one can use broadband time-resolved absorption spectroscopy techniques, which are traditionally based on incoherent light sources. They can provide an ultra-broadband time-resolved spectrum, but they need a long averaging time to achieve a high signal-to-noise ratio (SNR) and detection sensitivity. Two widely used methods are step-scan mechanical Fourier transform spectroscopy (FTS)5,6,7 and dispersion-based detection8,9,10,11. The former exhibits very long measurement times due to the step-scanning, while the latter yields shorter measurement times, but usually has a coarse spectral resolution.

In contrast to these traditional broadband methods, optical frequency comb spectroscopy (OFCS) simultaneously provides a broad spectral coverage and a high spectral resolution. It can also yield a high SNR within a short measurement time, due to the coherency and high spectral brightness of optical frequency comb sources. Specifically, OFCS in the mid-infrared (mid-IR) wavelength range (2–20 µm) has been of particular interest, since almost all molecules have their fundamental rotational-vibrational transitions in this region with distinct absorption patterns (i.e. fingerprints). Various OFCS techniques have been utilized in the mid-IR wavelength region; e.g. combining an optical frequency comb with a mechanical FTS12,13, dual-comb spectroscopy (DCS)14,15,16,17,18 and dispersion-based methods19,20,21,22. A comprehensive review of these spectroscopic methods can be found elsewhere23.

Monitoring of chemical reactions using OFCS in static or semi-static conditions can provide interesting results24,25,26, however the full potential of this technique would be exploited by time-resolved measurements. Time-domain/time-resolved spectroscopy using optical frequency combs with time resolutions well below second time scale has emerged strongly in the last decade. In a first demonstration, DCS was used for measuring molecular free induction decay in the near-infrared (near-IR) wavelength range using two Er:fiber mode-locked lasers27. A few other works have been reported in near-IR region using Ti:sapphire mode-locked lasers including dual frequency comb-based transient absorption (DFC-TA) spectroscopy for measurement of the relaxation processes of dye molecules in solution from femtosecond to nanosecond timescales28, and DCS for the study of laser-induced plasma from a solid sample, simultaneously measuring trace amounts of Rb and K in a laser ablation29. Er:fiber mode-locked lasers has also been used in time-resolved dual-comb spectroscopy (TRDCS) to monitor a fast, single shot reaction30 and also in continuous-filtering Vernier spectroscopy for combustion analysis31 both with milliseconds time scale resolution. In the visible range (~530 nm), cavity-enhanced transient absorption spectroscopy (CE-TAS) has been demonstrated for study of the ultrafast dynamics of I2 in a molecular beam32, and more recently, TRDCS has been reported for measurement of number density and temperature in a laser-induced plasma by monitoring three excited-state transitions of Fe33. In the mid-IR region, cavity-enhanced time-resolved frequency comb spectroscopy (TRFCS) is utilized for monitoring of transient free radicals and kinetics of the OD + CO → DOCO reaction by 2D cross-dispersion of the spectrum on a liquid N2 cooled camera using a virtually imaged phase array (VIPA) etalon in combination with a conventional grating3,34,35. Time-resolved dual-comb spectroscopy based on quantum cascade lasers (QCLs) has also been demonstrated in the mid-IR region. Generally, these spectrometers provide a shorter spectral bandwidth and coarser spectral resolution compared to mode-locked-laser-based spectrometers; however, they can provide a better time resolution. A single-shot sub-microsecond demonstration is reported for monitoring of protein reactions in the liquid phase36 and the same system is also used for monitoring of high-temperature reaction between propyne and oxygen in the gas phase37.

Here, we report time-resolved dual-comb spectroscopy (TRDCS) in the mid-IR wavelength region by nonlinear conversion of near-IR combs emitted from mode-locked lasers, and demonstrate its application for monitoring fast chemical dynamics. For this, we study the vibrational excitation/de-excitation of CH4 in an electrical discharge and the concentration of the reaction product C2H6, at millisecond and microsecond time scales, while the discharge is modulated between dark and glow regimes.

Results

Dual-comb mid-IR spectrometer

The dual-comb spectrometer (Fig. 1) is based on a femtosecond singly-resonant optical parametric oscillator (OPO) containing two nonlinear crystals in a single cavity. The crystals are synchronously pumped by two Yb:fiber mode-locked lasers (counter propagating and cross polarized) with a stabilized repetition rate (frep) difference of ∆frep ≈250 Hz and free running carrier-envelope offset frequencies (fceo)38,39. The two mid-IR idler beams (~3.3 μm) are combined on a beam splitter producing two pairs of beams. One pair is transmitted through a ~50 cm-long discharge tube (diameter 3 mm, water-cooled) containing CH4 diluted in He, and focused onto a fast photodetector. The discharge tube has a continuous gas flow (4 normal liter/hour, 4 Nl/h) and is connected to a gas handling system. The second comb pair is sent through a reference absorption cell (filled with CH4 at low pressure) and dispersed by a diffraction grating. A part of the spectrum is focused on a second photodetector to monitor a single well-defined absorption line of the reference sample. The time-domain interferograms in the output of the two photodetectors are digitized, a Blackman apodization function is applied to the both (sample and reference) interferograms, and followed by a Fourier transformation to yield the corresponding absorption spectra. The apodization function is used to minimize the ringing effect around the (narrow) absorption lines40, which also limits the effective measurement time-window of each interferogram to ~120 μs around the central burst. Therefore, each individual interferogram is measured in 120 μs with a repetition period of 1/∆frep (≈4 ms). The absorption line in the spectrum of the reference gas is used to correct for the frequency jitter in the sample spectrum, which is mainly due to the free running fceo values; it also provides an absolute optical frequency calibration. The free-running fceo of the two combs makes the experimental setup much less complex compared to the state-of-the-art, fully stabilized, mid-IR dual-comb spectrometers, which are also capable of recording full interferograms in milliseconds time scale16,17. Note that although a longer measurement time-window can theoretically provide a better spectral resolution; however, it is not practical in our system due to the short coherency time of the two idler combs caused by free running fceo values. In other words, a measurement time-window more than 120 µs would cause the average spectrum to be broadened and distorted. A detailed discussion about this issue as well as the explanation of the data acquisition and signal processing of the optical referencing method can be found elsewhere40 and a more detailed description of the experimental setup is presented in the Methods section.

Figure 1
figure 1

Experimental setup. Two femtosecond Yb:fiber lasers with stabilized and slightly different frep (and free running fceo), synchronously pump two MgO:PPLN crystals in a single OPO cavity, providing two mid-IR idler beams. The two combined idler beams are sent through the sample (discharge) cell and a reference gas cell. The latter yields the dual-comb spectrum of a single well-defined absorption line, which is used to correct for the free running fceo, as well as absolute frequency calibration of the sample spectrum. M flat mirror, M1-4 concave dielectric mirror, CM flat chirped dielectric mirror, DM dichroic mirror, BD beam dump, BS beam splitter, λ⁄2 half-waveplate, L lens, PD photodetector, LPF low pass filter.

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To demonstrate the performance of the spectrometer, we filled the discharge cell with 50% CH4 diluted in He, at 25 mbar total pressure and a total flow rate of 4 Nl/h, and measured the transmission spectrum without the discharge. Figure 2a shows the normalized transmission spectrum of the fundamental CH4 transition from the ground state to the ν3 vibrational state (in black, 500 averages, ~2 s measurement time, offset for clarity). To achieve normalized spectrum, we divided the transmission spectrum of the sample to an averaged background spectrum. The background spectrum was measured when the discharge cell was filled by pure He at 25 mbar. We developed a theoretical model spectrum of CH4 (in blue, inverted and offset for clarity) based on the HITRAN database41 parameters and a Voigt profile, convolved with a Blackman instrument line-shape function (corresponding to the applied apodization function). To achieve the CH4 concentration, we fit the model spectrum to the measurement with CH4 concentration as the fitting parameter, and also take into account the remaining baseline and etalon fringes by including a sum of a low order polynomial and few low frequency sinewave functions in the fit. The retrieved CH4 concentration is 49.7(9)%, where the error is the standard deviation of 10 consecutive measurements. We obtained a spectral resolution of ~6 GHz (~0.2 cm−1), with an absolute precision of ~120 MHz (~0.004 cm−1). The residual of the fit is shown in Fig. 2b, indicating the good agreement between the measurement and the model, however some structures remain in the residual which are mainly due to the comparable precision of the frequency calibration to the unapodized absorption linewidths. To estimate the absorption sensitivity per spectral element, we take the ratio of two consecutive background (pure He) spectra and fit and remove a baseline as in the treatment of the absorption signals described above. The noise at ~3020 cm−1 is σ = 1.3 × 10−2 at T = 8 ms, and considering interaction length of L = 50 cm and number of resolved elements equal to M = 1335 (=267 cm−1/0.2 cm−1), the absorption sensitivity per spectral element, calculated as σ/L(T/M)1/2, is equal to 6.4 × 10−7 cm−1Hz−1/2.

Figure 2
figure 2

Measured spectrum without discharge. (a) Normalized transmission spectrum of 50% CH4 diluted in He at 25 mbar total pressure and room temperature (black, 500 averages), along with a fit model spectrum of CH4 (in blue, inverted and offset for clarity) using HITRAN database parameters. (b) Residual of the fit.

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Methane spectrum in a static discharge

We measured the normalized transmission spectrum of the aforementioned gas sample (50% CH4 in He, 25 mbar) in a static discharge. We applied a DC voltage of 10 kV and a stabilized current of 10 mA (current density 1.4 mA/mm2) to the discharge tube and kept a constant sample gas flow of 4 Nl/h through the cell. Figure 3a shows the measured normalized spectrum of the sample with the discharge (in red, 500 averages, ~2 s measurement time) compared to the measured normalized spectrum of the sample without the discharge (in black, 500 averages, ~2 s measurement time). Note that, neither a baseline correction nor an etalon-fringes removal process is applied to these spectra to demonstrate that no particular artifact is added to the spectrum due to the discharge. In the discharge the CH4 absorption is reduced, which indicated a lower population in the vibrational ground state, due to vibrational excitation, ionization and molecular dissociations. This is accompanied by the appearance of two groups of additional absorption lines in the spectrum with the discharge, enlarged in Fig. 3b,c. The additional absorption lines in Fig. 3b are due to the produced C2H6 in the discharge. Since the C2H6 model in the HITRAN database is incomplete, we measured the room temperature absorption spectrum of 10% C2H6 diluted in He (25 mbar total pressure) in order to obtain a proper reference spectrum for C2H6. We fit the retrieved reference spectrum to the recorded discharge spectrum, with the concentration of C2H6 as the fitting parameter. This fitted spectrum is shown in Fig. 3b (in blue, inverted for clarity), and the retrieved C2H6 concentration from the fit is 6.52(11)%. Note that, we excluded few C2H6 absorption lines from the broadband fitting routine, since they showed deviation from the corresponding absorption lines in the reference spectrum, most probably due to differences in number densities at these levels caused by the discharge. The second group of additional absorption lines, indicated by “*” in Fig. 3c, are due to vibrational hot band transitions in CH4, since CH4 molecules are excited in the discharge. Many more (weaker) hot band absorption lines appear in all three P-, Q-, and R- branches, but are not highlighted in the figure. The first vibrational excited state of CH4 is ν4 (energy level ~1310 cm−1) followed by ν2 (energy level ~1533 cm−1). The majority of the detected hot band absorption lines undergo a vibrational ν3 + ν4 ← ν4 transition and a smaller portion originate from the ν3 + ν2 ← ν2 transition. All hot band ro-vibrational transitions can be assigned using the HITRAN database.

Figure 3
figure 3

Methane spectrum in the discharge. (a) Normalized spectrum with the discharge (in red, 500 averages) compared to the normalized spectrum without the discharge (in black, 500 averages). (b) An enlargement to the absorption lines of C2H6 produced in the discharge compared to a fitted room temperature spectrum of C2H6 (in blue, inverted). (c) An enlargement to a number of stronger rotational lines (indicated by ‘*’) within the hot band transitions of CH4.

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Time-resolved measurement at milliseconds time scale

To perform time-resolved measurements, we modulated the current of the discharge, with a square-wave function in an “off” (dark) and “on” (glow) regime (20% duty cycle for “on” time). The current modulation was synchronized with the repetition rate difference (∆frep ≈250 Hz) of the dual-comb spectrometer, and the modulation frequency, fmod, was chosen to be equal to ∆frep divided by 100, i.e. fmod = ∆frep/100 (≈2.5 Hz). Therefore, each period of the discharge modulation was recorded by a set of 100 consecutive interferograms, each at its own time-bin (more details in the Methods section). This allowed averaging of the spectra (after Fourier transform of the interferograms) for each corresponding time-bin of different discharge cycles to achieve high SNR averaged spectra. Therefore, we monitored each period of the discharge modulation with a time resolution equal to the inverse of ∆frep, i.e. Tres = 1/∆frep (≈4 ms). We obtained the normalized spectra of the gas sample (50% CH4 in He, 25 mbar, flow rate 4 Nl/h) over the entire period of the modulation (400 ms) with a time-resolution of 4 ms. Figure 4a shows the retrieved concentrations of the generated C2H6, and Fig. 4b demonstrates the absorbance of R(7) line at ~3082.2 cm−1 corresponding to the vibrational ν3 + ν4 ← ν4 hot band transition of CH4, as an indicator of the number of excited CH4 molecules. The discharge was turned on and off at t = 0 ms and t = 80 ms, respectively. The corresponding values at each data point is retrieved from an averaged spectrum measured in 1 s (250 averages), hence the total measurement time for the entire data set (containing 100 data points) is 100 s. Note that we began to record the data after the modulation was applied for a few minutes, in order to avoid any possible transient conditions from a static to a dynamic regime.

Figure 4
figure 4

Time-resolved measurement at milliseconds time scale. (a) Concentrations of generated C2H6 and (b) absorbance of the R(7) rotational line at ~3082.2 cm−1 in the vibrational ν3 + ν4 ← ν4 hot band of CH4, with 4 ms time resolution, recorded while the discharge is switched between dark and glow regimes. Different states of the discharge are separated by red dashed lines and are indicated by red “On” and “Off” labels.

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As shown in Fig. 4a, after turning the discharge on at t = 0 ms, the concentration of C2H6 increases from 0.71% to 2.4% in ~20 ms and reaches to a pseudo-plateau region. The absorbance of the hot band line abruptly appears at t = 0 ms, as shown in Fig. 4b, not resolvable with the current (4 ms) time resolution. After this abrupt appearance, the absorbance demonstrates a decrease to half of its initial value in ~20 ms and reaches to a pseudo-plateau region. The comparable time scale in the increase of the C2H6 concentration and decrease of the hot band absorbance suggests that these two processes are likely to be correlated. After the discharge is turned off at t = 80 ms, the C2H6 concentration increases instantaneously from 2.5% to 6.7%, while the hot band transition disappears. None of these two processes can be resolved with 4 ms time resolution. After the sudden increase, the C2H6 concentration decreases linearly, within the gas refresh time of the long and narrow discharge cell, before it reaches a pseudo-plateau region slowly decreasing from 1.0% to 0.71% by the end of the cycle. The latter demonstrates the remaining C2H6 molecules in the discharge cell most probably due to purging inhomogeneity.

Time-resolved measurement at microseconds time scale

To perform time-resolved measurement at microseconds time scale, the square-wave current modulation was synchronized with ∆frep, with an equal frequency fmod = ∆frep (≈250 Hz), while the current modulation could be deliberately time-delayed (phase-shifted) with respect to ∆frep (more details in the Methods section). For each particular time-delay the consecutive interferograms were recorded and directly averaged after Fourier transform to yield a high SNR spectrum. To cover the period of the current modulation, the time-delay was step-scanned and an averaged spectrum was measured for each step. In this configuration the time resolution is equal to the time-delay steps (e.g. 20 μs); however, for rapid changes happening faster than the measurement time of each individual interferogram (120 μs), the measurement results would be smoothened by a moving average. We obtained the normalized spectra of 50% CH4 in He (25 mbar, flow rate 4 Nl/h) over the entire discharge modulation period of 4 ms (square-wave function, ~10% duty cycle for “on” time). The step size was 20 μs near the switching events and 50 μs far from the switching events. Figure 5a shows the generated C2H6 concentrations and Fig. 5b demonstrates the absorbance of the same CH4 hot band line of R(7) at ~3082.2 cm−1, that was previously monitored in the millisecond time scale. Data are shown for a time span of 1 ms around the 400 μs period that the discharge was on. The corresponding values at each data point is retrieved from an averaged spectrum measured in 1 s (250 averages), hence the total measurement time for the entire data set (containing 42 data points) is 42 s, excluding the standby time for varying the time-delay.

Figure 5
figure 5

Time-resolved measurement at microseconds time scale. (a) Concentrations of generated C2H6 and (b) absorbance of the R(7) rotational line at ~3082.2 cm−1 in the vibrational ν3 + ν4 ← ν4 hot band of CH4, with 20 μs time resolution, recorded while the discharge is switched between dark and glow regime. Different states of the discharge are separated by red dashed lines and are indicated by red “On” and “Off” labels.

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In contrast to the results obtained in the milliseconds time scale, no discontinuity of the monitored parameters is observed in the microseconds time scale measurements. Note that after applying the current modulation to the discharge, the system operated for a few minutes before recording the data, to avoid any possible transient conditions from a static to a dynamic regime. Due to the high frequency of the discharge modulation the gas flow is insufficient to purge the generated C2H6 on each modulation cycle, which leads to an accumulation of C2H6 up to a concentration of 7.7% just before the discharge is turned on, as shown in Fig. 5a. When the discharge is turned on at t = 0 μs, the C2H6 concentration initially decreases rapidly to 3.0% in ~100 μs, after which it increases slightly to 3.2% in the next 300 μs. This slight increase reflects early-time dynamics, observed at the milliseconds time scale measurements right after turning the discharge on. In Fig. 5b, the absorbance of the monitored hot band line demonstrates a rapid increase to a comparable amplitude that has been observed with the milliseconds time scale measurements. The rise time is ~60 μs, which is faster than the observed fall time of the C2H6 concentration. After the rapid formation of the hot band line, the absorbance amplitude is slowly decreased from ~7.5 × 10−3 cm−1 to ~6.5 × 10−3 cm−1, right before the discharge is turned off. This is in agreement with the observed decay dynamics in the milliseconds time scale measurement, following the initial abrupt increase. After the discharge is turned off, the C2H6 concentration increases from 3.2% to 7.6% in ~500 μs. Meanwhile, the absorbance of the monitored hot band line decreases to zero in ~200 μs. The dynamics of the vibrational excited CH4 and the generated C2H6 are opposing each other, with the former slightly faster than the latter. The dynamics of C2H6 implies that when the discharge is turned on, it dissociates the C2H6 into free radicals, such as C2H5˙ and CH3˙, while after the discharge is turned off these radicals recombine, and amongst others, form C2H6. This interpretation also explains the abrupt increase of C2H6 concentration after the discharge was turned off in the milliseconds time scale measurements (Fig. 4b at t = 80 ms).

At these pressures in the discharge, we can also observe that the dissociation (formation) of C2H6, to (by recombination of) free radicals is slower than vibrational excitation (de-excitation) of CH4 molecules. The vibrational de-excitation of methane is mainly due to the collisions. We measured the collisional de-excitation decay time of different rotational lines in the hot bands, by fitting exponential functions to the absorbance of the hot band lines (after the discharge is turned off).

Figure 6 shows the corresponding measurements and fits for absorbance of three rotational hot band lines, R(2) at ~3043.9 cm−1 and R(7) at ~3082.2 cm−1 corresponding to the vibrational ν3 + ν4 ← ν4 hot band transition, and R(8) at ~3091.4 cm−1 corresponding to the vibrational ν3 + ν2 ← ν2 hot band transition. The hot band ro-vibrational transitions were assigned using the HITRAN database. The collisional de-excitation decay times retrieved from the fits are 57(5) μs, 52(3) μs, and 54(2) μs, respectively. Although the decay times are shorter than the measurement time of each individual interferogram (120 μs), they are not affected by the moving average, since the shape and decay rate of an exponential function will not be affected by integration. This is also evident by the good agreement between the measurements and the fit exponential functions.

Figure 6
figure 6

Collisional de-excitation of three hot band lines. The rotational lines are R(2) at ~3043.9 cm−1 (red squares) and R(7) at ~3082.2 cm−1 (blue diamonds) in the vibrational transition of ν3 + ν4 ← ν4, as well as R(8) at ~3091.4 cm−1 (black circles) in the vibrational transition of ν3 + ν2 ← ν2 of CH4. The time-resolved absorbance is demonstrated along with an exponential fit to each data set. The retrieved decay times form the fits are shown in the figure legend.

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Conclusion

We demonstrated the capabilities of time-resolved dual-comb spectroscopy (TRDCS) in the mid-IR wavelength range based on nonlinear conversion of near-IR combs emitted from mode-locked lasers. For this, we studied the vibrational excitation and de-excitation of CH4 in a modulated electrical discharge and its reaction product C2H6 at milliseconds and microseconds time scales. The total acquisition time for each measurement was in the order of tens of seconds. The spectrometer covered a wavelength range from ~3.1 μm to ~3.4 μm with a spectral resolution of 6 GHz and a single shot acquisition time of ~120 μs. By tuning the OPO light source, it is possible to monitor the other wavelength ranges from 2.7 μm to 4.7 μm. In this initial demonstration of TRDCS, we observed the products at %-levels due to the relative short interaction path length. The detection sensitivity of the spectrometer can be enhanced by using a multipass arrangement or an enhancement resonant cavity. Higher detection sensitivity, in combination with the broad spectral tunability of the OPO, provides the possibility to monitor less abundant interesting species in the discharge process in different wavelength ranges, e.g. free radicals, transient species and ions. In the dynamics, a wealth of information becomes available, which we only scratched the surface in this first demonstration. A comprehensive time-resolved study of a discharge process for the kinetics of reactions and branching next to temperature information could be feasible. The system can also be used for studying any fast chemical reaction that can be periodically triggered with an acceptable level of reproducibility. Finally, it should be noted that DCS has an inherent trade-off between the measurement time and the spectral resolution, which provides flexibility to choose a proper combination for each particular application. The minimum measurement time can be deliberately selected to be the shortest time with which the spectral resolution is still sufficient for detecting the desired species and/or resolving the target spectral features.

Methods

Optical setup

The two mid-IR frequency combs are generated from a singly-resonant optical parametric oscillator (OPO) based on two MgO:PPLN crystals (Covesion Ltd., UK) positioned in a common OPO cavity. Each crystal is synchronously pumped by a Yb:fiber mode-locked laser (Menlo Systems, Germany) emitting around 1040 nm. The pump beams are counter propagating in the ~3.3 m-long OPO cavity and are perpendicularly polarized. The repetition rates (frep) of the mode-locked lasers are ~90 MHz and stabilized to a common reference clock but are slightly different (∆frep ≈ 250 Hz), yielding the repetition rate difference in the generated idlers combs. The carrier-envelop offset frequency (fceo) of the two pump mode-locked lasers as well as the OPO cavity length are not stabilized. Each idler beam can provide up to 200 mW of average power, covering a wavelength range of around 350 nm, and is tunable from 2.7 to 4.7 μm using different poling periods in the nonlinear crystals. The two idler beams (after polarization adjustment) are combined by a beam splitter to produce two pair of beams on reflection and transmission. One pair is transmitted through the discharge tube, filled with CH4 diluted in He at a total pressure of 25 mbar. The transmitted beams are focused on a fast (50 MHz) thermoelectrically cooled HgCdTe photodetector (PVI-4TE, Vigo System, Poland), detecting the down-converted RF interferogram. The second pair is transmitted through a reference absorption cell, containing pure CH4 at 100 mbar, and is dispersed by a diffraction grating. A small part of the dispersed spectrum, containing a single well-known absorption line of CH4 (at 3038.498 cm−1), is focused on a second HgCdTe photodetector (PVI-4TE, Vigo System, Poland). The outputs of the two detectors are recorded by a two channel 125 MSam/s, 16 bits, analog-to-digital convertor (NI-5762, National Instruments, US) and saved on a computer for data processing. A common 10 MHz clock is used to synchronize the dual-comb spectrometer, the data acquisition, and the modulation of the discharge current.

Data processing and averaging

Each of the recorded interferograms is Fourier transformed to reconstruct the spectrum. The free running carrier envelope offset frequencies and unstabilized OPO cavity length reduce the complexity of the experimental setup, but they cause a changing frequency shift in consecutive recorded spectra. Since the fluctuations of the offset frequencies and the OPO cavity length are negligible in the measurement time of a single interferogram (120 μs), i.e. the two idler combs are coherent in this time scale, a linear frequency shift is sufficient to correct for these changes in each single measurement. To address this frequency shift, we use the frequency position of the known reference absorption line and correct the frequency shift of each individual spectrum before averaging, which also yields an absolute optical frequency calibrated spectrum. The spectra are averaged after the shift correction.

Discharge setup and modulation

The Pyrex discharge tube is ~50 cm long, with an internal diameter of 3 mm and it is water cooled. The hollow cathodes are at the two ends of the tube and the anode is at the center. A current-stabilized high-voltage (HV) power supply (Haefely Hipotronics, US, providing up to 25 kV, 40 mA) is used for generating a DC discharge in the tube. The power supply is able to limit the current overshoots during switching/modulation of the discharge. The discharge can be switched on (glow) and off (dark) by modulating the current of HV power supply using a signal generator, whose clock is synchronized with the repetition rate different (∆frep) of the dual-comb spectrometer. The modulation signal is a square-wave whose frequency, duty cycle, and time-delay (with respect to the ∆frep) can be adjusted independently. Therefore, the data acquisition and discharge process are synchronized and can also be programmed to have a time delay with respect to each other. The timing schematic of the discharge modulation with respect to the DCS interferogram is shown in Fig. 7(a) for millisecond and Fig. 7(b) for microsecond time scales.

Figure 7
figure 7

Timing schematic for discharge modulation with respect to the DCS interferogram in (a) millisecond and (b) microsecond time scales.

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