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Abstract
Mid-infrared (MIR) dual-comb spectroscopy (DCS) is a highly effective method for molecular metrology of rovibrational transition spectra in a quick accurate manner. However, due to limited comb frequency instability, manipulating coherence between two frequency combs to accomplish high-quality spectral analysis in the MIR region is a huge challenge. Here, we developed a comb-teeth resolved MIR DCS based on active phase control cooperating with a CWs-dependent (CWD) interferogram timing correction. Firstly, four meticulously engineered actuators were individually integrated into two near-infrared (NIR) seed combs to facilitate active coherence maintenance. Subsequently, two PPLN waveguides were adopted to achieve parallel difference frequency generations (DFG), directly achieving a coherent MIR dual-comb spectrometer. To improve coherence and signal-to-noise ratio (SNR), a CWD resampled interferogram timing correction was used to optimize the merit of DCS from 7.5 × 105 to 2.5 × 106. Meanwhile, we carried out the measurement of MIR DCS on the methane hot-band absorption spectra (v3 band), which exhibited a good agreement with HITRAN by a standard deviation on recording residual of 0.76%. These experimental results confirm that this MIR DCS with CWD interferogram timing correction has significant potential to characterize the rovibrational transitions of MIR molecules.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Dual-comb spectroscopy (DCS), employing a pair of coherent optical frequency combs (OFCs) with a slight difference in repetition rate frequency (fr), is a significant optical-frequency measurement method that can parallelly collect thousands of optical frequency information through coherent multiple heterodyne interference. Since the demonstrations [1–5], the DCS has spawned much attention in a large number of same-concept experiments, offering a more excellent option for rapid high-resolution high-accuracy spectral metrology in the fields of molecular characterization [6,7], trace gas sensing [8–11], multidimensional coherent atom spectrum [12,13] and absolute distance measurement [14,15]. Compared to conventional Fourier transform infrared (FTIR) spectrometers, the DCS can accomplish broadband frequency spectroscopy using a single radio-frequency photoelectric detector without any mechanical movement stage, in which the resolution, accuracy, and speed of measurement are mainly determined by coherence between two OFCs rather than the mechanical instruments. Taking the advantages, a series of potential DCS-based spectroscopy applications, including both linear [16–18] and nonlinear [12,13,19–21] processes, have been demonstrated in the infrared (NIR) region. To scale up the sensitivity, the DCS has already been extended to the MIR region [22,23] for the larger spectral absorption cross sections of rovibrational transition and high-quality transmissivity in the atmosphere window, successfully analyzing multispecies trace gas molecular [24]. Nevertheless, a significant challenge lies in identifying practical gain materials for the direct generation of stable mode-locked mid-infrared (MIR) pulses. This challenge renders conventional phase-frequency locking methods, typically applied to near-infrared (NIR) combs, unavailable when extending operations to the MIR range.
To acquire stable MIR combs, numerous methods have been proposed via interband cascade laser (ICL) [25], micro resonators [26–29], fluoride fibers [30], optical parameter oscillators (OPO) [31], optical parameter amplification (OPA) [32], difference frequency generation (DFG) [23,33,34], and electro-optic modulators (EOM) [35]. Among these methods, the DFG is particularly competitive in constructing MIR DCS system for the broadband phase-matching spectrum and simple structure [36]. Moreover, the process of DFG converts phase and frequency manipulation of the MIR comb to the driving pump and signal NIR combs with a mature OFC controlling scheme [37–40]. Nevertheless, phase and frequency noise accumulations are inevitable at the frequency conversion, especially in the broadband DFG process where the frequency linewidth of generated MIR DCS can’t be kept up with the driving NIR sources. Moreover, the signal and pump combs accumulate additional noises arising from power scaling, nonlinear spectral broadening, and DFG, which will mainly lead to the coherence degeneration of the MIR DCS. For improving the mutual coherence of MIR DCS, some effective methods have been demonstrated. The common approach is employing an ultra-stable MIR CW to acquire the relative frequency jitters, then the active OFC controlling scheme can also be used to reduce the relative frequency jitters for coherence enhancement. Meanwhile, the potential of the passive approach to coherent MIR DCS has been proved using a single CW laser as an intermediary assisted with EOM [35] and optical-optical modulators [41]. Also, single-cavity dual-comb systems [42] offer the intrinsic advantage of passive mutual coherence and can be considered for mid-infrared comb generation. In addition, several phase correction techniques [43–46] and algorithms [47,48] have been adopted to overcome the impression of these cumulative phase and frequency noises, achieving mode-resolved DCS. J. Genest’s group developed dual-comb spectrometers in which interferograms were continuously corrected and averaged in real time [45,46]. Although many schemes are proposed to accomplish the DFG MIR DCS, the coherence and phase noise still need to be further optimized for the applications of high-SNR high-sensitive high-accuracy broadband MIR molecular spectroscopy.
In this study, we demonstrate a DFG-based MIR dual-comb spectrometer using active phase control cooperating with CWs-dependent (CWD) digital phase correction. The MIR double combs were obtained through the DFG process in high-efficiency chirped PPLN waveguides driven by the NIR dual-comb sources, in which the active coherence of DCS was maintained via making use of four-dimensional actuators in oscillator cavities. Due to the residual noise that still existed after active phase locking affecting long-time measurements, digital interferogram timing correction was needed to improve the measurement accuracy of the system. To further improve the coherence and SNR of MIR DCS, two CWs at 1030 and 1560 nm were employed as intermediary frequency sources to acquire the real-time NIR phase jitters of the injected pump and signal combs. Based on the real-time phase jitters, we constructed a digital phase correction to resample the DCS data in the MIR region, compensating for the accumulated phase noise introduced in frequency conversion, fiber transmission, and power scaling. After the CWD digital interferogram timing correction, the merit of the dual-comb spectrum with 33637 comb teeth was improved from 7.5 × 105 to 2.5 × 106. This system was evaluated through a high-SNR MIR molecular hot-band absorption spectroscopy on methane gas, in which the standard deviation of the recording residual between the measured DCS spectrum and HITRAN database is only 0.76%. Considering the sufficient coherence, high SNR, and high resolution of the MIR DCS, we believe that it will be a competitive method for quantitative analysis of gas types and concentrations in the MIR region.
2. Experiment setup
2.1 Optical self-reference NIR dual-comb seed source
Figure. 1 shows the scheme of coherent NIR combs (Master comb and slave comb), which was employed as seed combs for the MIR comb. Specifically, both the NIR combs were constructed with a nonlinear amplifier loop mirror (NALM), directly emitting two trains of mode-locked ultrashort pulses around 1560 nm. In oscillators [39], four well-designed actuators, including piezoelectric transducer (PZT), pump current, phase-modulating electrooptical modulator (PM-EOM), and amplitude-modulating electrooptical modulator (AM-EOM), were adopted for high-precise phase feedback and coherence control. The carrier-envelope offset frequencies (fM,CEO and fS,CEO) of two combs were locked to 20 MHz via a combination frequency control of corresponding AM-EOMs and pump powers. For the stabilization of repetition rate frequency (fM,r and fS,r), the master comb repetition frequency was directly detected by a photodetector from the oscillator output, and then direct phase locked to a 100 MHz standard reference generated from the Hydrogen clock. Then the slave combs employed a CWD frequency detection loop (FDL1) to acquire a relative frequency difference (Δfb,1560) between two combs, which was also locked to 20 MHz via cooperated PM-EOM and PZT in the slave comb.
Fig. 1. The scheme of coherent NIR dual-comb seed sources. fM,CEO and fS,CEO: Carrier-envelope offset frequency; fM,r and fS,r: repetition rate frequency; CW1 and CW2: 1560-nm and 1030-nm continuous wave lasers; APD: avalanche photodiode; FDL: frequency detection loop; fb1,1030, fb2,1030, fb1,1560, and fb2,1560: the beating frequencies between CWs and combs; Δfb,1030: frequency difference between fb1,1030 and fb2,1030; Δfb,1560: frequency difference between fb1,1560 and fb2,1560; DFG: difference frequency generation.
As the FDL1 part shown in Fig. 1, a 1560-nm CW laser (CW1) was used to produce dual-comb beating frequencies (Δfb,1560) at 1560 nm, which could be described as:
2.2 Coherent DFG-based MIR dual-comb interferometer
As shown in Fig. 2, the MIR dual-comb spectrometer consists of four parts, including two coherent NIR combs, two parallel PPLN-based DFG, a gas cell, and the interference sampling analysis. The NIR dual-comb source was coherently controlled through the scheme depicted in Fig. 1. To accomplish DFG for obtaining MIR combs, the pulse trains from the NIR comb were divided into two branches: pump and signal beams. The pump branch with the power of ∼200 mW was delivered into an 8-cm HNLF for spectral broadening, directly emitting a supercontinuum spectrum ranging from 1 to 1.7 µm, as shown in Fig. 3(a). Subsequently, the pump pulses were optically filtered to ∼1064 nm with a 1064 nm fiber bandpass filter. And they were further amplified to ∼150 mW in an Yb-doped fiber amplifier (YDFA) with full width at half maximum (FWHM) of 29 nm, as described in Fig. 3(b). Figure. 3(b) shows that the 220-mW signal branch was centered at 1560 with a FWHM of 31 nm. The signal and pump pulses were combined using a dichroic mirror and focused into a PPLN waveguide by a lens with a focal length of 8 mm, generating 1.5-mW mid-infrared light ranging from 3 to 4 µm, as depicted in Fig. 3(b). Moreover, the PPLN waveguides were designed with a waveguide channel of 15 µm and a chirped aperiodic period of 23–32 µm.
Fig. 2. The schematic of the MIR dual-comb spectrometer. HNLF: highly nonlinear fiber; YDFA: Yb-doped fiber amplifier; DM: dichroic mirror; PPLN: periodically polarized lithium niobate; BS: beam splitter; BPD: balanced photodiode; DCS: dual-comb spectroscopy; PC: personal computer; DAQ: data acquisition; fClock: Hydrogen Clock.
Fig. 3. (a) Supercontinuum spectrum generated in a piece of anomalous dispersion HNLF for pump light. (b) The spectral properties of pump comb, signal combs, and DFG-based MIR comb.
In principle, the MIR optical frequency comb (fMIR) generated by DFG is described as:
2.3 CWs-dependent phase correction for high-SNR dual-comb spectroscopy
To expound the theory of CWD dual-comb digital phase correction, we depict a detailed scheme demonstration in Fig. 4. Firstly, the beating optical fields (Eb1,1560 (t), Eb2,1560 (t), Eb1,1030 (t), and Eb2,1030 (t)) between CWs and combs can be described as:
Because of that the fM,CEO and fS,CEO were both locked to 20 MHz, we ignored the CEO jitter (dfCEO) in EΔb,1560 (t) and EΔb,1030 (t). Based on the injected pump (EΔb,1030 (t) and signal (EΔb,1560 (t) comb fields, we can calculate the DFG dual-comb optical beat frequency (EΔb, MIR (t)) by Eq. (2) as:
Through subsequent functions of filter and angle, we can obtain the DFG dual-comb optical field phase:
Finally, we employ function to unwrap φΔb,MIR, and perform resampling of EDCS,MIR (t). After the resample, all the DFG MIR DCS comb line were phase correction and reference to φΔb,DFG, which was obtained by optical-reference EΔb,1030 (t) and EΔb,1560 (t). The fluctuation of different repetition rates is corrected, which is described as:
Fig. 4. The CWD phase correction scheme for MIR DCS. EDCS (t) and E’DCS (t): MIR DCS optical fields; Eb1,1560 (t), Eb2,1560 (t), Eb1,1030 (t), and Eb2,1030 (t): the beating optical fields between combs and CW lasers; EΔb,1560 (t), and EΔb,1030 (t): dual-comb beating optical fields at 1030 nm and 1560 nm; EΔb,MIR (t), and φΔb,MIR (t): the calculated optical field and phase of DFG dual-comb beating frequency in MIR.
Experimentally, we obtained NIR dual-comb beating frequencies (Δfb,1560 and Δfb,1030) at 1560 nm and 1030 nm via circuit mixers, as shown in Fig. 1. And a Fast Fourier transform (FFT) spectrum analyzer was used to characterize the Δfb,1560 and Δfb,1030, whose relative line profiles are depicted in Figs. 5(a) and (b) at 1 s time window. The optical frequency beatings between the two combs were 24.1 and 20 MHz, respectively. Obviously, the SNR of theΔfb,1560 is much higher than the Δfb,1030 while the linewidth is much broader. This is partly due to the fact that the 1.0-µm pump comb experienced more nonlinear transmitting including HNLF and YDFA than the 1.5-µm signal comb, which caused the degenerations of dual-comb coherences in phase and frequency, and exhibited SNR declining and linewidth broadening. A circuit mixer was chosen to simulate the difference frequency in the optical field, then we got a reconstructed MIR frequency (Δfb,MIR) at 44.1 MHz, which contained the coherence of the pump and signal combs. Therefore, we can use the reconstructed frequency to resample the MIR DCS, helping to correct the line shape of the MIR comb teeth for high-SNR spectral analysis. To accomplish high-quality phase correction, all the frequencies (Δfb,1030, Δfb,1560, and Δfb,MIR) were acquired using a fast data acquisition card, as shown in Fig. 2.
Fig. 5. (a) The measured NIR dual-comb beating frequencies (Δfb,1560 and Δfb,1030) at 1560 nm and 1030 nm. (c) The reconstructed MIR frequency (Δfb,MIR) via a circuit mixer.
3. Results and discussion
The CWD phase correction is an appropriate method to improve the linewidth and SNR of the MIR comb teeth. To evaluate the effects, we separately measured the MIR DCI spectrum at cases with and without phase correction. Figure. 6 shows a segment of the DCS spectrum with a measurement time of 2 s, where the DCS sample signal was Fourier transformed with 1-fold zero padding and no apodization. As shown in Fig. 6(a), we enlarged the frequency window to 2 kHz in the radio frequency domain, in which the frequency interval was consistent with the 145.66-Hz repetition frequency difference. When we continued to enlarge the frequency window to 100 Hz, it is noticed in Fig. 6(b) that the SNR was improved by a large margin as from 4.2 to 44.9 while the linewidth was compressed to 1 Hz from 2.1 Hz. Moreover, the ground noise of the RF DCI spectrum decreased after the phase correction, giving an improvement to SNR. Benefiting from phase correction, the typical sideband elimination was also clearly observed in single comb tooth. These improvements on linewidth and SNR evidentially confirm the effective effects of phase correction on the compensation for phase noise introduced in the DFG process.
Fig. 6. (a) The uncorrected (red line) and corrected (blue line) MIR DCS. (b) The linewidth of uncorrected (red line) and corrected (blue line) MIR DCS.
Figure 7 shows the comb-teeth resolved MIR DCS with and without digital phase correction. A typical time-domain interference signal with a 100-ms temporal window was collected via a BPD, as shown in Fig. 7(a). And the time interval among interferograms is equal to 6.865 ms, corresponding to a repetition rate difference of 145.66 Hz. Using the fast data acquisition, we captured a total of 77 DCIs at a 528-ms recording time. Then, these DCIs were transformed frequency domain through FFT, helping to obtain the DCS. After coherent averaging of 450 times over 237 s, we achieved a comb-teeth resolved quantitative analysis of the DCS spectrum, as depicted in Fig. 7(b). As we can see, there is a noticeable bulge at the bottom of DCS, which is mainly caused by the cumulative phase noise. In detail, considering the line profile of the NIR comb tooth (As insertion in Fig. 5), every comb tooth of the MIR DCS had the same line profile with two symmetry modulation sidebands. When carrying out long-time averaging, this modulation sideband overlapped to form a bulge on the DCS ground, which degraded the frequency accuracy and SNR. It is noticed that the bulge at the bottom is completely removed in the new DCS with the phase correction, which corresponds to the phenomenon of sideband elimination and linewidth suppression on single comb tooth observed in Fig. 6(b). Significantly, the average SNR with a measurement time of 1-s even increased to 75.1 from the uncorrected 22.5 due to removing of the bulge on DCS ground. Thus, the figure of merit of DCS, defined as SNR × M/T1/2, increased from 7.5 × 105 to 2.5 × 106 after phase correction, where T represents the measurement time, and M represents the number of comb teeth determined by spectral width, which is 33637. Subsequently, we enlarged the corrected MIR DCS to the partial spectral windows of typical methane absorption at P, Q, and R branches, as shown in Figs. 7(c), 7(d), and 7(e), respectively. It is observed that there is an obvious offset intensity at the bottom of uncorrected DCS. And this valid phase correction reset the offset intensity to zero, which would facilitate the high analysis for molecular concentration. Figures 7(b), 7(d), and 7(e) characterize the fine structure of the CH4 absorption spectrum, further confirming the availability of the 100-MHz resolution CWD MIR DCS.
Fig. 7. (a) The raw data of DCI. (b) The MIR DCS with (blue) and without (red) phase correct (red). Typical absorption of methane (CH4) in the P branch (c), Q branch (d) and R branch (e) with (blue) and without (red) phase correction.
To verify the ability for molecular spectroscopy, we demonstrated a high-resolution high-SNR MIR DCS on methane gas. An 8-cm gas cell was employed as sample container, which was filled with methane gas at a pressure of 0.8 mbar. Using a beam splitter (BS), two MIR comb beams were combined into the gas cell with a single-pass path of 8 cm. An optical filter with a bandwidth of 150 nm at 3.3 µm was placed in front of the gas cell to filter out stray light. Through the DAQ sample and FFT, we obtained the transmitted MIR DCS of methane with 100-MHz resolution. Figure 8 shows the comparison between the measured results and the theoretical profile from the HITRAN [49] database. Considering that the standard deviation of the residual is only 0.76%, we believe this DCS result is in good agreement with that of methane line parameters in the HITRAN. Figure 8(a) shows the spectra with a single period with 36000 averaging times. When we continued to increase the average times to 36000, the relative SNR at transmitted peak was scale up to 1882. The experimental results proved that this DCS system have important potential to the quantitative analysis of gas types and concentrations in the MIR region.
Fig. 8. (a) Transmitted DCS spectra after removing the background averaging 36000 times. (b) Transmitted spectra of HITRAN 2020. (c) The residual between DCS and HITRAN.
4. Conclusion
In conclusion, we demonstrate MIR DCS with resolved comb teeth by combining active phase control, DFG, and CWD digital phase correction. Four high-precision phase locking loops were used to control the coherence of two NIR combs, from which the pump and signal lights originated. Then two PPLN crystals were separately adopted to two parallel DFGs for achieving a coherent MIR dual-comb spectrometer. Moreover, the CWD digital phase correction employed two CW lasers as probers to monitor the mutual coherence of the NIR dual-comb source, and resampled the MIR DCS data to compensate for the phase noises introduced in the HNLF broadening, fiber amplifier, and PPLN-based DFG, providing a convenient effective way to improve the merit of DCS from 7.5 × 105 to 2.5 × 106. To evaluate the capacity of molecular metrology, we measured the hot-band absorption MIR DCS spectrum on the v3 band of the methane, exhibiting a good agreement with the HITRAN database for the 0.76% standard deviation of the residual. In the future, we hope that this MIR DCS will be used to characterize the rovibrational transitions of MIR molecules.
Funding
National Natural Science Foundation of China (12134004, 12204178, 12104162, 12274141).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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