2. Experimental setup and results

The schematic of the MIR comb generation is shown in Figure 1, which includes a seed comb centered at 1.5 μm, an Er-doped fiber amplifier, a prism compressor, an HNLF, and an IPDFG module. The seed comb based on an Er-doped fiber mode-locked laser emitted a pulse train with 1 mW average power and a 100 MHz repetition rate. The average pulse power was scaled up to 328 mW using a bidirectionally pumped fiber amplifier, in which a 3 m Er-doped single-mode fiber with a normal dispersion was used as the gain medium. A pair of silicon prisms was adopted to provide controllable anomalous dispersion for pre-chirp management of SCG. Linearly polarized light was injected into the dispersion prisms at a Brewster angle to reduce the reflection loss on the prism surfaces. Behind the prism compression, a 300 mW laser was coupled to a collimator with a 12 cm PM1550 pigtail fiber, which could further recompress the pulse duration. Figures 2(a) and 2(b) show the autocorrelation curve and spectrum after the prism compressor, respectively. The pulse duration is 92 fs with sech² fitting, and the spectrum covers the range from 1520 to 1620 nm. The large pulse wings are caused by uncompensated nonlinear chirp. A 3 cm PM HNLF with an anomalous dispersion of 1.9 ps/(nm·km) was employed to generate a supercontinuum spectrum. The spectral broadening and soliton self-compression processes in the anomalous-dispersion HNLF were adjusted using the prism-based pre-chirp management module.

Figure 4 (a) Schematic of the MIR dual-comb system. The recorded interferograms at different time scales of (b) 150 ms and (c) 0.02 ms. CW, continuous-wave laser; BPD, balanced photodetector; DAQ, data acquisition.

To drive the IPDFG and yield MIR light, the supercontinuum from the HNLF was directly coupled to a chirped PPLN waveguide. The HNLF is placed on a three-axis stage to launch light to the waveguide. A zoom lens and a camera system on the top of the waveguide were used for high-magnification imaging. By adjusting the stage, we can get the optimal alignment and measure the output light. The mode diameter of the HNLF is 3.5 μm. This PPLN waveguide is 15 μm wide and 25 mm long with aperiodic periods of 23–32 μm that were consistent with our previous study^[ Reference Zhou, Liu, Lou, Di, Xie, Zhu, Deng, Luo, Gu, Chen and Li ^{35 ]}. The coupling efficiency is 60%. In general, some spatial optical components, including wedge and chirp mirrors, were required to control the pulse chirp before IPDFG^[ Reference Lesko, Timmers, Xing, Kowligy, Lind and Diddams ^{26 ,} Reference Hoghooghi, Xing, Chang, Lesko, Lind, Rieker and Diddams ^{28 ]}. These extra spatially manipulated modules increased total loss and system complexity. In particular, we did not adopt common methods for controlling the chirp but simply adjusted the prism pair before the anomalous-dispersion HNLF to optimize the temporal alignment of pump-signal pulses with the soliton self-compression effect^[ Reference Xing, Lesko, Umeki, Lind, Hoghooghi, Wu and Diddams ^{27 ,} Reference Travers, Grigorova, Brahms and Belli ^{36 –} Reference Li, Yao, Jia, Wang, Qin, Ohishi and Qin ^{38 ]}. In addition, these prisms could be removed completely to simplify the system for integrated MIR comb generation^[ Reference Iwakuni, Okubo, Tadanaga, Inaba, Onae, Hong and Sasada ^{31 ]}. Thereafter, a gold-coated off-axis parabolic mirror with a focal distance of 6 mm collimated the light to free space. Finally, a long-pass filter at 2.4 μm was used to filter out the residual pump and signal light, outputting an MIR frequency comb with high transmissivity.

To characterize the spectral evolution of the SCG and IPDFG, we measured the corresponding spectral profiles using two commercial spectrometers (Yokogawa AQ6370 and Bristol 771B). The HNLF delivers a 150 mW supercontinuum with a spectral range of 1–2 μm, as shown in Figure 3(a). Theoretically, this supercontinuum spectrum can provide the pump and signal light for 2–5 μm idler generation. In addition, absorption lines were observed at approximately 1900 nm owing to water vapor in the air. To maximize the conversion efficiency of the IPDFG, the slow axis of the HNLF was rotated to ensure that the pump and signal lights were coupled to the waveguide with vertical polarization. After the filter, 0.7 mW MIR light was obtained. The spectrum was measured using a Fourier-transform spectrometer (Bristol 771B) with a 33 GHz spectral resolution, as shown in Figure 3(b). We observed that the long wavelength was cut off at 4.2 μm, which was not as broad as expected. The most likely reason is that the waveguide channel brought different group velocity dispersions to the pump and signal pulses, which caused temporal misalignment of the pump and signal pulses. In addition, the effect of waveguide dispersion on the refractive index is ignored, so the poling periods are not optimal. In future studies, dispersion engineering and poling periods should be considered to redesign the waveguide and broaden the MIR spectrum^[ Reference Jankowski, Langrock, Desiatov, Marandi, Wang, Zhang, Phillips, Lončar and Fejer ^{39 ]}. We measured the relative intensity noise (RIN) of the MIR light, as shown in Figure 3(c). The integrated RIN is 0.87%.

Figure 5 Mode-resolved MIR dual-comb spectra at different wavelength scales of (a) 1.4 μm, (b) 0.002 μm and (c) 0.0002 μm.

A dual-comb spectrometer based on the IPDFG method was constructed for DCS measurement, as shown in Figure 4(a). Two Er-doped fiber comb systems served as the seed combs. The NIR local comb (f _{0_comb1} = 20 MHz and f _{r_comb1} = 100 MHz) was referenced to the hydrogen maser clock. A 10 Hz linewidth continuous-wave (CW) laser centered at 1560 nm (OE4030, OEwaves) was referenced to the local comb to provide a standard optical frequency reference for the signal comb. To stabilize the signal comb, the carrier-envelope-phase offset frequency (f _{0_comb2} = 20 MHz) and the optical beat note were locked. Moreover, two electro-optic modulators were used in the signal oscillator to improve the modulation bandwidth of the frequency control^[Reference Deng, Liu, Zhu, Luo, Gu, Zhou, Xie and Li^{40 ]}. Thereafter, two combs were delivered into two parallel IPDFG modules to generate the MIR dual-comb system. The two MIR combs could provide a broad spectrum from 2.4 to 4.2 μm. To evaluate the applicability for spectroscopy, the two MIR beams were combined to pass through an 8 cm gas cell filled with pure methane at a pressure of 150 mbar. The interferogram signal was acquired through a balanced photodetector (Qube-DT, ppqSense) equipped with two HgCdTe photodetectors (PVI-2TE-5, VIGO System). The response spectral range of the detector is 3–5 μm. In addition, two half-wavelength plates were used to control the polarization of the MIR light and optimize the signal-to-noise ratio (SNR) of the interferograms. Before the detection, we attenuated the power of the signal comb to ensure that the two beams with the same power were injected into the detector. After passing through a 48 MHz electronic low-pass filter, the DCS signal was recorded using a data acquisition card with a sampling rate of 100 MHz. Figure 4(b) shows the measured interferogram signal for 150 ms. It is evident that the period of the interferograms was approximately 0.024 s, corresponding to the repetition rate difference of approximately 42 Hz. Figure 4(c) exhibits a 0.02 ms temporal domain of interferograms in which we can acquire the information in the frequency domain via further Fourier transform.

Figure 6 (a) Absorption lines of methane in the 3537–3547 nm region. (b) Zoom-in absorption line of methane at 3541.1–3541.3 nm. (c)–(e) Comparison results of the extracted gas absorption lines (blue dot) and the theoretical profiles from the HITRAN database (red line).

To retrieve the frequency-domain optical spectrum, 20 interferograms (0.5-s temporal signal) were extracted as a unit for the Fourier transform. To obtain a high SNR DCS, the frequency domain was coherently averaged by 208 times over 100 s. As illustrated in Figure 5(a), we obtained the DCS in the range of 3.0–4.2 μm, corresponding to a frequency bandwidth of 25 THz. The retrieved dual-comb spectrum was narrower than the spectrum measured using a Fourier-transform spectrometer because we could not retrieve the spectrum in the 2–3 μm range owing to the limited response bandwidth (3–5 μm) of the detector. In the frequency domain, approximately 2.5 × 10⁵ modes were resolved with a 100 MHz spectral resolution. We also calculated the figure of merit, defined as SNR × M / T ^1/2, where M is the number of comb teeth and T is the measurement time. The figure of merit was 1.03 × 10⁶, which is with the same order of magnitude as the results in Refs. [Reference Timmers, Kowligy, Lind, Cruz, Nader, Silfies, Ycas, Allison, Schunemann, Papp and Diddams30,Reference Ycas, Giorgetta, Friedlein, Herman, Cossel, Baumann, Newbury and Coddington41]. In addition, the SNR of the peak spectrum, which represents the ratio of the signal to random variations of the baseline^[ Reference Ycas, Giorgetta, Baumann, Coddington, Herman, Diddams and Newbury ^{21 ]}, was 28. Figures 5(b) and 5(c) show the mode-resolved MIR dual-comb spectra over wavelength spans of 0.002 and 0.0002 μm, respectively, confirming that the simple DCS system has the capacity for high-resolution gas sensing in the MIR region.

To assess the applicability of the MIR dual-comb system to high-resolution spectroscopy, we measured its methane absorption spectrum. Several absorption lines in the 3537–3547 nm region are shown in Figure 6(a). A single absorption peak zoom-in in the 3541.1–3541.3 nm range consists of approximately 50 comb modes with a frequency interval of approximately 100 MHz, as shown in Figure 6(b). Figures 6(c)–6(e) show several absorption peaks (blue dots), in which all the absorption lines are consistent with the standard profiles (red curves, Voigt profiles, HITRAN 2020^[ Reference Gordon, Rothman, Hargreaves, Hashemi, Karlovets, Skinner, Conway, Hill, Kochanov, Tan, Wcisło, Finenko, Nelson, Bernath, Birk, Boudon, Campargue, Chance, Coustenis, Drouin, Flaud, Gamache, Hodges, Jacquemart, Mlawer, Nikitin, Perevalov, Rotger, Tennyson, Toon, Tran, Tyuterev, Adkins, Baker, Barbe, Canè, Császár, Dudaryonok, Egorov, Fleisher, Fleurbaey, Foltynowicz, Furtenbacher, Harrison, Hartmann, Horneman, Huang, Karman, Karns, Kassi, Kleiner, Kofman, Kwabia-Tchana, Lavrentieva, Lee, Long, Lukashevskaya, Lyulin, Makhnev, Matt, Massie, Melosso, Mikhailenko, Mondelain, Müller, Naumenko, Perrin, Polyansky, Raddaoui, Raston, Reed, Rey, Richard, Tóbiás, Sadiek, Schwenke, Starikova, Sung, Tamassia, Tashkun, Vander Auwera, Vasilenko, Vigasin, Villanueva, Vispoel, Wagner, Yachmenev, Yurchenko and Quant ^{42 ]}). The RMSs of the residuals in Figures 6(c)–6(e) were 3.2%, 1.9% and 2.9%, respectively.

In the low SNR range, it is difficult to retrieve the absorption lines, although the SNR of our system can be further improved by increasing the power. The saturation power (~2 mW) of the detector limited the SNR because each comb line has only nW-level power. It remains a challenge for dual-comb systems to achieve high SNR DCS in broadband parallel measurement. Recent work has demonstrated a method of signal processing to resolve this issue in the NIR region, and the ideas could be used to improve the SNR of MIR DCS^[ Reference Guay, Walsh, Tourigny-Plante and Genest ^{43 ]}. In this system, the spectrum has a fast baseline with tens of gigahertz linewidth, which is a similar linewidth to that with the gas absorption line at standard or high atmospheric pressure. So, we measure the gas absorption peak at low pressure (150 mbar) to reduce the impact of the baseline. For broader absorption lines at standard atmospheric pressure, the four-point normalization correction method can be used to effectively remove the effects of the baseline^[ Reference Ycas, Giorgetta, Cossel, Waxman, Baumann, Newbury and Coddington ^{1 ,} Reference Ycas, Giorgetta, Friedlein, Herman, Cossel, Baumann, Newbury and Coddington ^{41 ,} Reference Rieker, Giorgetta, Swann, Kofler, Zolot, Sinclair, Baumann, Cromer, Petron, Sweeney, Tans, Coddington and Newbury ^{44 ]}.