1. Introduction

The optical frequency comb of a mode-locked laser, or simply called ‘comb’ hereafter, permits precision spectroscopy by making use of its dense comb-tooth lines [1–3]. Such comb-resolved spectroscopy was first put into practice by adopting a diffractive spectrometer made of gratings or prisms [4–7]. This dispersive form of comb spectroscopy is relatively easy to implement but its achievable spectral resolution is limited by the resolving power of the spectrometer that hardly reaches the common comb-tooth spacing of a hundred MHz or less. Fourier-transform spectroscopy using a comb was also implemented by equipping a two-arm interferometer with the capability of incremental scanning of the reference or measurement arm length [8,9], or alternatively with insertion of a long unequal optical path while sweeping the repetition rate of the source comb in control of its cavity length [10,11]. Both the Fourier-transform schemes of comb spectroscopy require a long length scanning mechanism over several meters to resolve the comb-tooth spacing. Meanwhile, asynchronous optical sampling by employing an additional comb of a slightly different repetition rate began to be widely investigated as it enables broad-band comb spectroscopy without troublesome time-consuming length scanning at all [12,13]. This dual-comb spectroscopy has now made a remarkable progress in theory and applications, evolving from a high precision laboratory tool of atomic lines observation [14–18] to an industrial means of multiple gas species in the open air [19–21].

It is also known that combining a comb with long-standing continuous wave (CW) laser spectroscopy allows the measurement accuracy and speed to be improved without excessive hardware complexity. An example is employing a comb as the optical frequency ruler for the real-time calibration of fast sweeping tunable laser spectroscopy [22,23]. Another example is incorporating a comb with a CW laser so as to produce comb-resolved multi-heterodyne beats only around a targeted absorption line without wavelength tuning [24–28]. Compared with dual-comb spectroscopy, this combined comb-CW-laser spectroscopy requires a wide radio-frequency measurement bandwidth since multi-heterodyne beats are sampled without down-conversion. In this investigation, motivated by the preceding attempts of combined comb-CW-laser spectroscopy, a new scheme named direct comb segmentation spectroscopy is proposed. This scheme is intended particularly for realization of rapid, comb-resolved detection of multiple molecular absorption lines that are remotely positioned but need to be traced simultaneously with a high signal-to-noise ratio (SNR). For the purpose, the probe comb is divided into several sub-comb segments through band-pass filtering around targeted absorption lines. The sub-comb segments are then coupled individually with CW lasers of which the frequency positions are phase-locked close to the targeted absorption lines. In consequence, for each targeted absorption line, an optimum number of multi-heterodyne beats are produced and subsequently handled with concerted data processing. The performance is verified by the simultaneous detection of two absorption lines of hydrogen cyanide (H¹³C¹⁴N) and carbon dioxides (¹²CO₂), remotely positioned with a spectral gap of 2.74 THz. In addition, atmospheric ¹²CO₂ concentration is traced over a 1.3 km open path to demonstrate the capability of fast, sensitive greenhouse gas monitoring in the presence of outdoor air turbulence.

2. Measurement principle

Figure 1 illustrates the opto-electronic system configured in this study to implement the proposed scheme of direct comb segmentation spectroscopy. Only a single comb is used as the probe comb, which is provided from an Er-doped fiber oscillator emitting ultrashort laser pulses of 150 fs duration. The N-th comb-tooth line is expressed a $f_N=N\times f_N+f_o$ with f_r being the pulse repetition rate and f_o being the carrier-envelop offset frequency. With reference to the Rb clock, the probe comb is stabilized by fixing at 100 MHz by regulating the oscillator cavity length using a piezoelectric actuator, and f_o at 40 MHz by control of the oscillator pump power while being monitored using an f-2f interferometer. With an average comb power of 200 mW boosted through an Er-doped fiber amplifier (EDFA), the probe comb is separated into multiple sub-combs by band-pass filtering using a fiber Bragg grating array (FBGA). Each sub-comb segment is allocated a 25 GHz spectral bandwidth and 0.1 mW optical power, and its center frequency is adjusted so as to target a specific molecular absorption line of interest within a tolerance range of 8 GHz. Basically, there is no restriction in the number of sub-comb segments to be used concurrently, but two segments are considered hereafter for the convenience of explaining relevant principles; one is centered at 1549.72 nm for detection of the P10 line of H¹³C¹⁴N (2ν₃ rotational-vibrational band) and the other at 1572.02 nm for the R18 line of ¹²CO₂ (30012←00001 rotational-vibrational band).

 

Fig. 1 System configuration of comb segmentation spectroscopy. DFB LD: distributed feedback laser diode, EDFA: erbium-doped fiber amplifier, FBGA: fiber Bragg grating array, f: frequency, f_r: repetition rate, f_o: carrier-envelop offset frequency, OFS: optical frequency synthesizer, PD: photo-detector, Rb: rubidium, ∆s: spectral width of comb segments, λ-meter: wavelength meter.

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For each sub-comb segment, a distributed feedback (DFB) laser diode (LD) is allocated as a CW optical line to produce multi-heterodyne radio-frequency (RF) beats in interference with adjacent comb-tooth lines. In order to reduce the phase jitter of multi-heterodyne beats, the LD is phase-locked to a pre-selected comb-tooth line within the sub-comb segment near the targeted absorption line. The phase-locked loop (PLL) control is performed using the Rb clock that offers a 10 MHz reference signal with a fractional stability of 10⁻¹¹ at 1 s. The LD’s phase-locked optical frequency is monitored at a 2 Hz update rate using an extra wavelength meter (Agilent, 86122A) pre-calibrated to provide a 20 MHz accuracy. Once all the LDs have been stabilized individually to their corresponding sub-comb segments, the resulting multi-heterodyne beats are converted to RF electric signals through a high-speed photodetector of a 25 GHz bandwidth (Newport, PD1414) and sampled using a high-speed digital oscilloscope at a 40 GHz sampling update rate (Agilent, DSO81304B). The collected RF data is then Fourier-transformed to a beat spectrum of an 8 GHz spectral bandwidth with a 100 kHz resolution. The whole sequence of sampling multi-heterodyne RF beats with subsequent Fourier-transform is repeated at every time interval of 10 μs.

Figure 2 illustrates the data processing procedure to measure two absorption lines of P10 of H¹³C¹⁴N and R18 of ¹²CO₂ simultaneously. The LDs are phase-locked to be $f_{{}_1}=N_1\times f_{{}_r}+f_o+\Delta f_1$ for LD₁ and $f_{{}_2}=N_2\times f_{{}_r}+f_o+\Delta f_2$ for LD₂ as depicted in the optical domain of Fig. 2(a). Note N₁ (N₂) indicates the mode number of the particular comb-tooth line to which LD₁ (LD₂) is phase-locked with a locking offset of Δf₁ (Δf₂). The RF beats created between the sub-comb segments and the LDs are down-converted in the RF domain as for k = 0,1,2,⋅⋅⋅ as plotted in Fig. 2(b). All the multi-heterodyne beats of $f_{{}_k}$ are identified by Fourier-transform, and they are distinguished into two groups: one for LD₁ with the condition of $f_{{}_k}=k\times f_{{}_r}\pm \Delta f_1$ and the other for LD₂ with $f_{{}_k}=k\times f_{{}_r}\pm \Delta f_2$. The LD locking offsets, Δf₁ and Δf₂, are selected as much different as Δf₁ = 20 MHz and Δf₂ = 30 MHz, so no confusion arises in the group sorting between LD₁ and LD₂. Lastly, the RF frequency f_k is up-converted to its original optical frequency around the nominal frequency of f₁ (f₂) for LD₁ (LD₂). The up-conversion procedure is such that the RF frequency of $f_{{}_k}=k\times f_{{}_r}-\Delta f_1(\Delta f_2)$is placed on the right-hand side of f₁ (f₂), while $f_{{}_k}=k\times f_{{}_r}+\Delta f_1(\Delta f_2)$ on the left-hand side of f₁ (f₂).

 

Fig. 2 Data sampling. (a) Multi-heterodyne interference between sub-comb segments and their corresponding CW laser lines in the optical frequency domain. (b) Electric beats sampled in the radio-frequency domain. ∆f₁: locking offset of DFB LD₁, ∆f₂: locking offset of DFB LD₂.

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Figure 3(a) presents the optical spectrum of the probe comb in overlap with those of the two LD lines measured with a 6.24 GHz (0.05 nm) resolution. The probe comb spectrum spreads its optical power broadly from 1520 nm to 1590 nm. The sub-comb segments are individually confined to narrow spectral ranges of about 25 GHz (FWHM) as shown in Figs. 3(b) and 3(c); the colored partitions indicate the multi-heterodyne ranges of a ± 8 GHz bandwidth used in the data processing described in Fig. 2. The two LDs phase-locked at 1550 nm (red) and at 1572 nm (blue) maintain a high frequency stability comparable to that of the Rb clock employed as the master clock for phase-locked loop (PLL). Specifically, the Rb clock used here is able to offer an absolute stability of 9.93 × 10⁻¹⁰ at 1 ms or 3.45 × 10⁻¹¹ at 1 s. The absolute stability was validated independently in our study through an elaborate beat test between two separate Rb clocks. The LDs’ optical frequencies are measured to hold a relative stability of 2.37 × 10⁻¹¹ at 1 ms or 7.26 × 10⁻¹³ at 1 s, being two orders of magnitude less than the absolute stability of the Rb clock as plotted in Fig. 3(d). This result implies that the absolute frequency stability of the LDs after phase-locking becomes close to that of the Rb clock. In consequence, the phase jitter of multi-heterodyne beats between the LDs and sub-comb segments is ~400 kHz (FWHM) as shown in Fig. 3(e). Further, the sub-comb segments were given an optical power of 30 μW per each, which is well below the dynamic range threshold of the photo-detector in use to guarantee linear optical-to-electrical conversion. On the other hand, each LD was set to offer a relatively strong power of 300 μW since the dynamic range threshold of the photo-detector is large for a CW laser. In consequence, the SNR of the multi-heterodyne electric signals turns out 33 dB and 35 dB at 1550 nm (red) and 1572 nm (blue), respectively, even the averaging time is taken as short as 10 μs. The measurement time can be further shortened, but it requires more strict stabilization of the LDs to the source comb if the SNR has to be maintained as high as 30 dB.

 

Fig. 3 Experimental data. (a) Optical spectra of the source comb (black line) and two DFB LDs (red & blue lines) measured using an optical spectrum analyzer of 6.24 GHz resolution (0.05 nm). (b) and (c) Individual optical spectra of two sub-comb segments at 1550 nm and 1572 nm. Shaded areas (red & blue) produce multi-heterodyne beats over a 16 GHz bandwidth. (d) Frequency stability measurements of the Rb clock (gray) and DFB LDs (red). (e) Heterodyne RF beats measured at a sampling time of 10 μs.

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3. Measurement results

Figure 4 presents the measurement result on two absorption lines of the P10 line of H¹³C¹⁴N and the R18 line of ¹²CO₂. The target gases were contained in a gas chamber that consists of a 15-cm long cell filled with 10 torr of H¹³C¹⁴N gas and an 80-cm long cell filled with 300 torr of ¹²CO₂ gas. As depicted in Figs. 4(b) and 4(c), the measured absorption profiles are constructed with a 0.8 pm wavelength resolution, corresponding to the mode spacing of 100 MHz of the probe comb. Each profile is Voigt-fitted for interpolation after being normalized with respect to the reference spectrum obtained from a void chamber arranged in parallel with the target gas chamber. A single profile measurement takes 10 μs, and spectral averaging is taken over 20 consecutive measurements for a total averaging time of 200 μs. The transmittance is measured to be 0.5673 for the H¹³C¹⁴N line (red) and 0.8949 for the ¹²CO₂ line (blue). The measurement repeatability of transmittance is affected by the total averaging time as presented in Fig. 4(d); in terms of the standard deviation, the repeatability turns out 1.3% for 10 μs averaging and improves to 0.33% at 200 μs averaging. The repeatability variation follows a rule $1/\sqrt{\tau }$ with τ being the averaging time. From the measured transmittance curve, the center wavelength is identified to be 1549.73054 nm for the H¹³C¹⁴N line and 1572.01847 nm for the ¹²CO₂ line, showing a small discrepancy of 0.02 pm and 0.07 pm respectively with respect to the certified reference values [29,30] with the correction of pressure-induced shift at 293 K.

 

Fig. 4 Simultaneous detection of two absorption lines. (a) HITRAN database of H¹³C¹⁴N and ¹²CO₂ from 1525 nm to 1585 nm. (b) & (c) Measured absorption line profiles of the P10 line of hydrogen cyanide (H¹³C¹⁴N) at 1549.73054 nm and the R18 line of carbon dioxide (¹²CO₂) at 1572.01847 nm with a sampling time of 200 μs. The comb-resolved spectral resolution is 0.8 pm. For comparison, the same absorption lines were measured using a tunable CW laser by scanning over a measurement time of 100 s (black). (d) Standard deviation of the measured transmittance with increasing the sampling time from 10 μs to 1 ms (orange dots). Gray dots indicate the tendency of $1/\sqrt{\tau }$.

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As far as the measurement uncertainty is concerned, the most influencing factor is found the absorption baseline distortion that is caused by the etalon effect of the gas chamber as well as the temporal fluctuation of the measured absorption profile with respect to the reference spectrum obtained from the void chamber. The measurement uncertainty is estimated by quantifying the raw point data scattering around the absorption baseline, of which the standard deviation turns out about 0.3% for the ¹²CO₂ line. Besides, our measurement result is independently verified by comparing with an extra result (black) obtained using a tunable CW laser spectrometer with a wavelength step of 0.08 pm. The transmittance is gauged 0.5667 and 0.8961, which appears to yield a slight difference of 0.06% and 0.12%, respectively, from our measurement result. This indicates that our measurement result is accurate even though the averaging time is as short as 200 μs while the spectral gap between the two measured absorption lines is as large as 22.3 nm in wavelength or 2.74 THz in frequency.

Figure 5 shows another test measurement carried out in the open air to monitor the atmospheric concentration of ¹²CO₂ over 12 hours. The outdoor test was conducted over an optical link comprising a 1.3 km round-trip path as illustrated in Fig. 5(a). One sub-comb segment of a 25 GHz bandwidth was sent out via a refractive telescope of a 50 mm aperture diameter and received via a Cassegrain type reflective telescope of a 250 mm aperture diameter. The 25 GHz bandwidth is wide enough to detect the absorption line subject to pressure-broadening. For beam return, a flat mirror of a 300 mm aperture diameter was installed on the rooftop of a building 650 m away from the receiving telescope. The sub-comb segment was launched with 50 mW optical power using an addition EDFA as shown in Fig. 5(b), with each comb mode being allocated 0.1 mW power. The returned optical power was about 10 mW, with 80% loss due to light scattering and beam divergence over the long atmospheric path. The returned beam was focused on a single-mode fiber and combined with the phase-locked LD₁ to produce multi-heterodyne interference as illustrated in Fig. 5(b). The RF electrical signal of Fig. 5(c) collected by the photo-detector shows a high level of intensity fluctuation induced by air turbulence during the open-air transmission. Its Fourier-transformed data in Fig. 5(d) reveals that atmospheric turbulent disturbance prevails for fluctuation frequencies less than 2.5 kHz. The RF signal sampling rate was accordingly chosen to be as fast as 5 kHz with a corresponding averaging time of 200 μs, which permits RF signal sampling to be made without being significantly disturbed by dominant low frequency noise components.

 

Fig. 5 Outdoor measurement of atmospheric CO₂ concentration. (a) Measurement path of a 1.3 km round-trip distance. (b) Overall measurement system setup. (c) Temporal fluctuation of the received beam intensity due to air turbulence. (d) Power spectral density of the received beam intensity. (e) Absorption spectrum obtained at 200 μs sampling. (f) Measurement plots over 12 hours (green) in comparison with those of NDIR sensors (red). Error bars indicate uncertainty. (g) Measurement standard deviation with increasing the averaging time from 10 μs to 200 μs. Gray dots and dotted line indicate the tendency of $1/\sqrt{\tau }$.

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A transmittance profile measured at 22:00, June 23, 2017 in Fig. 5(e) shows an absorptance of 0.101, from which the concentration of ¹²CO₂ is estimated to be 466.5 ppm using the HITRAN 2012 molecular spectroscopic database [31,32]. For this calculation, the temperature was assumed 303.73 K, the pressure 0.987 atm, and the path length 1.3 km. The ¹²CO₂ density measurement was continued over 12 hours and compared with those monitored by three pre-calibrated nondispersive infrared (NDIR) sensors installed separately along the outdoor optical link. The NDIR sensors offered a measurement accuracy of ± 3% as depicted with red error bars in Fig. 5(f). The measurement uncertainty of our comb spectroscopy was estimated from the measurement repeatability at a 200 μs sampling time as given in Fig. 4(d). As shown with green error bars in Fig. 5(f), the absorptance strength at each measurement predicted that the measurement uncertainty lies from 13.3 ppm at 23:00 to 14.2 ppm at 09:00 in the next day. The measurement repeatability varies with the averaging time, from 55.7 ppm at 10 μs averaging to 13.3 ppm at 200 μs averaging. The $1/\sqrt{\tau }$ sampling rule indicates that further increasing the averaging time to 30 ms would reduce the standard deviation to 1 ppm as plotted in Fig. 5(g).

4. Conclusions

We have performed fast comb spectroscopy by employing sub-comb segments so as to produce multi-heterodyne beats focused around targeted molecular absorption lines. This concentrated scheme of comb spectroscopy proved to be able to achieve a 30 dB signal-to-noise ratio with just a single shot measurement of 10 μs acquisition time. The performance was verified by measuring two separate absorption lines of H¹³C¹⁴N and ¹²CO₂ gases and atmospheric ¹²CO₂ concentration over a 1.3 km open-air path. This target-specific scheme will facilitate diverse applications of comb spectroscopy as a rapid means of molecular detection with high signal sensitivity.