1. Introduction

Laser absorption spectroscopy has been successfully applied for research in atomic and molecular physics, chemistry, biology and frequency metrology for many years. Still, there are areas for improvement which could benefit science and industry, for example, the development of fast monitoring methods for trace gas concentrations could advance the modelling of climate change [1,2], or the detection of many different molecules in real-time could help in the diagnosis of diseases via biomarkers in human breath [3–5]. Along with the development of optical frequency combs (OFCs) in the mid-infrared (mid-IR) spectral range, there has been an advancement in molecular spectroscopy since many species have fundamental absorption bands in this fingerprint region [6,7]. Some of them may require constant monitoring of their concentrations, as they are detrimental to human life as well as the environment. Hydrocarbons are examples of gases with a high impact on our planet, as some of them, like methane (CH₄) and ethane (C₂H₆), are classified as greenhouse gases [8].

OFCs provide an exceptional combination of wide wavelength coverage and high spectral resolution, enabling accurate simultaneous measurements of broad spectral regions in short acquisition times, together with multispecies detection with a single light source [9–14]. Several detection methods have been developed to take advantage of the comb properties. One group of methods is based on Fourier transform spectroscopy (FTS), using either a Michelson interferometer with a mechanical stage [15–18] or a second comb with a slightly different repetition rate that resembles the effect of a fast-scanning delay line (so-called dual-comb spectroscopy) [19–21]. The second group uses dispersive methods like a virtually imaged phased array (VIPA) [22,23] or a mode-resolved Vernier spectroscopy [24,25]. An advantage of FTS over spectrometers based on dispersive elements is the wide simultaneous wavelength coverage with a single detector, not limited by the coatings of the optical dispersive elements. Moreover, with proper sampling, the resolution of comb-based FTS is given by the comb mode linewidth, which allows measuring undistorted high-resolution spectra [26–28].

In laser-based spectroscopy measurements, the signal strength depends on the interaction path length between a gas sample and a light beam. So far, the most common means for increasing the interaction length have been multipass cells (MPCs) [29,30] or optical cavities [31–33]. Despite being suitable for low-concentration gas sensing, these conventional methods require bulk optics, which must be precisely aligned, introduce losses with every mirror reflection, and are sensitive to temperature drift and mechanical vibrations. Superior sensitivity was achieved using optical frequency combs and cavities [17,33,34], however, cavity-enhanced schemes require precise control of comb-cavity frequency matching [35], which increases the complexity of the system. Additionally, a large sample volume of measured gas is required in such cells, which is not always available. A method that allows measuring samples with limited availability, such as the radioisotope samples, is photoacoustic spectroscopy (PAS) [36]. Approaches based on continuous-wave (CW) lasers are sensitive and fast but measure only a single absorption line, which limits their usage to single-species detection [37,38]. Mid-IR comb-based mechanical FTS has been combined with cantilever-enhanced PAS to allow broadband detection in the molecular fingerprint region [39,40]. The downside of this method is the measurement time of the order of a few minutes. More than 10 times faster acquisition with mid-IR comb-based PAS was obtained by replacing the conventional FTS with phase-controlled FTS, albeit at the expense of reduced performance [41]. Various fast and sensitive methods of comb-based PAS have been developed using the dual-comb approach, but they were all implemented in the near-IR spectra range around 1.5 µm [42–46].

An alternative and auspicious solution has recently been presented with the development of a novel type of microstructured optical fibers with the ability to guide light in air, the so-called antiresonant hollow-core fibers (ARHCFs) [47]. Benefiting from an essentially empty core, ARHCFs can be filled with the target gas sample and subsequently used as low-volume gas absorption cells that provide a several tens of meters long interaction path length between the laser and the sample [48,49]. Another exceptional advantage of ARHCFs is the bandwidth of their transmission window, which can span several hundreds of nanometers, especially in the mid-IR [47,50]. The ability to transmit light over a broad spectral range opens the possibility for ARHCFs to be employed in laser-based gas sensors targeting multiple species and/or complex molecules with broad spectra. Up to date, most of the work performed within the area of gas sensing using ARHCFs utilized narrow-linewidth CW coherent light sources (e.g., distributed feedback diode lasers, quantum cascade lasers, interband cascade lasers) in combination with various laser-based spectroscopic techniques usually targeting only one transition of a single gas within the near- or mid-IR spectral range. Nikodem et al. [48] demonstrated an ARHCF-based gas sensor utilizing well-established wavelength modulation spectroscopy (WMS) and tunable diode laser absorption spectroscopy (TDLAS) for detection of carbon dioxide (CO₂) in a 1.35 m long fiber. The sensor was capable of detecting CO₂ concentrations far below its atmospheric level. In another work, Yao et al. [51] used a more advanced technique, the so-called photothermal spectroscopy, in which the ability of an ARHCF to guide light in two dissimilar transmission windows was crucial. In this case, the target formaldehyde (H₂CO) was excited at 3.6 µm, and the spectroscopic signal was retrieved at 1.56 µm, which is very convenient from the sensor configuration and data analysis point of view. Jaworski et al. successfully utilized two dissimilar low-loss transmission bands of an ARHCF [50] and the ability to use a several-tens-of-meters long ARHCF as a gas absorption cell [49]. In both sensors, the WMS technique was used to extract the spectroscopic signal. The ARHCF used in these experiments could simultaneously guide light with low loss in the vicinity of 3.4 µm and 1.575 µm, which allowed simultaneous detection of methane (CH₄) and CO₂ within the ARHCF core [50]. Furthermore, the use of a 30-meter-long mid-IR guiding ARHCF resulted in the development of an ethane (C₂H₆) sensor with superb sensitivity at sub-parts-per-billion by volume level [49]. In addition, the results reported in [52–54] have proven that properly designed ARHCFs can be successfully used for gas molecule detection in the wavelength range of up to 10.5 µm.

Excellent results obtained within the area of ARHCF-based detectors of single gases have motivated the researchers to explore this technology and combine ARHCFs with broad optical sources, i.e. OFC lasers. Wang et al. reported in [55] the development of a near-IR acetylene (C₂H₂) sensor based on a dual-comb photothermal spectroscopy technique and a gas absorption cell formed by a 7-cm-long ARHCF. The sensor could retrieve multiple transitions of C₂H₂ simultaneously over approximately 10 nm around 1.535 µm. However, none of the research work published to date reported using ARHCFs for detection of complex and spectrally broad gases, e.g., hydrocarbons (pentane, butane, etc.), benefiting from one of the most valuable advantages of ARHCFs – very broad low-loss transmission bands, in particular within the mid-IR spectral range.

In this work, we present for the first time a combination of a mid-infrared optical frequency comb and an antiresonant hollow-core fiber capable of measuring sub-mL sample volumes of spectrally broad gases in the molecular fingerprint region with high sensitivity. The results for different hydrocarbons were compared to the ones obtained in the multipass cell of comparable length. The ARHCF outperformed the MPC regarding introduced losses, transmission rate and required gas sample volume. We show that the ARHCF offers almost 3 dB less transmission loss than MPC, which results from the losses on multiple reflections from the cell’s mirrors and can be crucial for low-power sources to obtain sufficient sensitivity. Significant reduction of the sample gas volume and the stability of ARHCFs make them promising low-volume, robust gas cells with long optical paths.

2. Experimental setup

The experimental setup is shown in Fig. 1. The setup can be divided into three parts: the comb source, the gas cell part with ARHCF and MPC of similar lengths, and the system for acquiring the output spectra. The setup started from a home-built fiber-based OFC with a central wavelength of 1565 nm and a repetition rate of 125 MHz. The mid-IR light was achieved by the nonlinear process of difference frequency generation (DFG) in a periodically poled lithium niobate (PPLN) crystal. The oscillator output was divided into two separate branches, and in one of them, it was blueshifted to the wavelength of around 1 µm. Both amplified branches were co-aligned and focused on a PPLN crystal, and, as a result of the DFG process, a mid-IR broadband beam was obtained. Its central wavelength could be tuned between 2900 cm⁻¹ (3450 nm) and 3400 cm⁻¹ (2940 nm). The details of the DFG source are described in Ref. [13].

 

Fig. 1. Schematic of the gas detector consisting of a mid-IR optical frequency comb (OFC) based on difference frequency generation in a χ⁽²⁾ nonlinear medium, antiresonant hollow-core fiber (ARHCF) and multipass cell (MPC) that could be selected using flip mirrors (FMs), and a Fourier transform spectrometer (FTS).

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In the next step, mid-IR light was sent into one of the gas cells, which could be chosen using flip mirrors. The power of the DFG source for the measurements equalled 18 mW, measured before the first flip mirror. In the first arm of the gas cells’ setup, we placed the ARHCF. The ARHCF that forms a gas absorption cell was fabricated from a high-purity fused silica glass preform (Suprasil F300) with the aid of a well-known stack-and-draw technology [50,56]. The final fiber structure consisted of a hollow core with a diameter of ∼84 µm. The core border was defined by the set of seven circular capillaries with an internal diameter of ∼54 µm, forming the fiber cladding area. The total diameter of the fiber was ∼318 µm. Since the light guidance principle in this type of hollow-core fiber can be described by the Antiresonant Reflecting Optical Waveguiding effect (ARROW), the thickness of the capillaries’ (core) walls is the crucial parameter, which defines the guided wavelength range of an ARHCF [57]. In the case of our fiber, which was designed to operate in the ∼3.4 µm spectral region, the thickness of the core wall was at the level of ∼1 µm. As a result, the fiber was characterized by an effective and low-loss transmission window covering approximately 900 nm in the mid-IR. The transmission characteristic of the ARHCF, together with a scanning electron micrograph (SEM) image of its cross-section and a near-field profile of the beam delivered at 3.34 µm, are presented in Fig. 2. The fiber attenuation at 3.34 µm was determined using the cut-back technique, and it reached a level of 0.03 dB/m [50]. Fiber loss was approximately 1.5 and 4.2 times lower compared to commercially available fluorozirconate (ZBLAN) and fluoroindate (InF₃) solid core mid-IR fibers, respectively [58].

 

Fig. 2. Simulated transmission spectrum of the ARHCF in the mid-IR spectra band. The insets on the graph represent an SEM image of the ARHCF’s cross-section (left) and fiber-delivered near-field beam profile at 3.34 µm, confirming light guidance in the LP01 mode.

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In order to form an ARHCF-based gas absorption cell, the 26.15(5) m long fiber was air-tightly closed at both ends by UV glueing it to self-designed and developed SWAGELOK-based gas chambers [49]. Both chambers were closed with barium fluoride (BaF₂) wedged windows, allowing light coupling into and out of the ARHCF. The total volume of the developed gas absorption cell was ∼0.77 mL, which is more than 1000 times less compared to the bulk optics-based multipass cell placed in the other arm of the setup. The fiber was kept coiled (coil diameter of 35 cm) during the entire experiment. The gas exchange process of the ARHCF was based on the overpressure-aided technique described in detail in Ref. [43]. The empty core of the ARHCF was completely filled within 100 seconds with the target gas mixture with a total pressure of 5 bar, which was subsequently equalized to the ambient value (740 Torr) by simultaneously exposing both ends of the fiber (with opened gas filling chambers) to laboratory air. After approximately 15 min of time required to obtain a stable gas pressure level within the fiber (measured with precise gas pressure meters – MKS 902B placed at both ends of the fiber), the flow of the target gas mixture through the ARHCF was initiated by increasing its pressure within the hollow region of the fiber to 850 Torr. The gas flow through the fiber was maintained constant throughout the measurements. The light from the OFC source was coupled into the fiber using a single plano-convex calcium fluoride (CaF₂) lens with a focal length of 50 mm, allowing the required match with the numerical aperture (NA) of ∼0.03 of the ARHCF. After transmission through a nitrogen (N₂) filled ARHCF, the optical power of the OFC beam was reduced to 2.85 mW. The total loss, which is a combination of fiber attenuation over its multimeter length, light coupling into and out of the ARHCF and bending loss, reached the level of 8 dB.

For the conventional method, the light was coupled using a CaF₂ plano-convex lens (focal length equal to 500 mm) into a commercially available Herriot multipass cell (Thorlabs, HC30 L/M-M02) with an optical path length of 31.227(20) m and 0.85 L volume. An additional 250 mm CaF₂ lens was used to collimate the light at the cell’s output. The power after the multipass cell was equal to 1.47 mW, which corresponds to 10.8 dB of total loss. The losses result from 80 internal reflections on the mirrors, which at the wavelength of 3.3 µm have reflectance at the level of ∼98.6%, as well as light coupling to the MPC and transmission values for the CaF₂ windows. Throughout the measurements, the gas sample pressure was kept at the level of 850 Torr, and the gas flow was maintained constant.

The light beam exiting either the MPC or ARHCF was directed into a home-built FTS with a design similar to the one in Ref. [13,17]. The spectrometer was based on a Michelson interferometer, with balanced detectors consisting of MCT photodiodes (model PVI-4TE-10.6, Vigo Photonics). Alongside the comb beam, a 1.55 µm laser diode beam was coupled into the FTS as a calibration for the optical path difference. The measurements were performed with a spectral resolution of 500 MHz, and the duration of one measurement was 1.67 s. First, the gas cell used for measurements at that time (ARHCF or MPC) was purged with N₂ to measure the reference spectrum and then filled with a sample gas to acquire its spectrum. The reference and sample measurements were performed 100 times, and subsequently, the interferograms were submitted to the Fast Fourier Transforms (FFTs) and averaged. Next, the sample spectrum was normalized to the reference spectrum, and the remaining baseline was removed using the cepstral method [59]. The absorption coefficients were computed using the Lambert-Beer law. The models for fits were calculated using the absorption lines parameter from the HITRAN database [60] and the Voigt profile or the absorption cross-sections from the Pacific Northwest National Laboratory (PNNL) database [61], with the concentration as the only fitting parameter.

3. Experimental results

3.1 Comparison of gas cells

In the first step, to compare the performance of the ARHCF and the MPC, we investigated the similarity between the transmission spectra through both gas cells filled with N₂. In Fig. 3(a) and (b), we show the transmission spectra of the DFG-based source through MPC and ARHCF, respectively, together with the difference between the two spectra in the lowest panel. Both spectra were first normalized to their peak intensity. Figure 3 proves good compatibility of the spectra with each other and, most importantly, confirms proper beam collimation into the hollow-core fiber. The absorption lines which can be observed in both spectra come from water vapor in the laboratory air filling the FTS. The structure visible in the residuals comes from etalon effects in both cells.

 

Fig. 3. Comparison of transmission spectra of the DFG-based comb through (a) antiresonant hollow-core fiber (ARHCF) and (b) multipass cell (MPC), both filled with N₂, together with the residuals, measured by the Fourier transform spectrometer.

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3.2 Measurements of individual molecular species

To demonstrate the vast possibilities of combining the optical frequency comb with antiresonant hollow-core fiber and Fourier transform spectrometer, we recorded spectra of various molecular species in the 2900 cm⁻¹ to 3050 cm⁻¹ spectral range. We chose four different hydrocarbons as molecules critical to climate change, two with resolvable lines at atmospheric pressure and two with broadband continuous absorption spectra. All gas cylinders were certified and contained gases with concentrations: 2.08 ppmv of methane (3% uncertainty), 1.07 ppmv of ethane (10% uncertainty), 9.64 ppmv of butane (5% uncertainty) and 10.26 ppmv of pentane (3% uncertainty). Figure 4 shows measured spectra (in black) of methane (Fig. 4(a) and (b)), ethane (Fig. 4(c) and (d)), butane (Fig. 4(e) and (f)) and pentane (Fig. 4(g) and (h)). Each plot also presents the fitted spectrum (in red and negative for clarity) using data from HITRAN or PNNL databases and the fitted value of the concentration. The residuals are plotted in the lower panel for every figure. Additionally, the division of the figure into two columns can help distinguish the spectra of the gas samples measured in the ARHCF and the MPC. The left column (Fig. 4(a), (c), (e) and (g)) represents spectra measured using the ARHCF, while the right column (Fig. 4(b), (d), (f) and (h)) shows spectra out of MPC. These measurements illustrate the ability of ARHCFs to be used as gas cells in the same way as multipass cells. Due to their wide transmission windows, they can cover broad spectral regions just as well as standard multipass cells. It is essential to notice that it is possible to measure gases with continuous absorption bands like butane and pentane without any errors from baseline drifts, as we are able to acquire all data at once and extract concentrations regardless of the structure of the absorption spectrum.

 

Fig. 4. Absorption spectra measured using a DFG-based OFC and FTS (black) at 850 Torr in the ARHCF and MPC, compared to fits based on HITRAN or PNNL database (red, plotted in negative for clarity). The residuals of the fits are shown in the lower panels of every figure. The gas type and concentration are designated in the panels: (a) and (b) 2.08 ppmv of methane (CH₄); (c) and (d) 1.07 ppmv of ethane (C₂H₆); (e) and (f) 9.64 ppmv of butane (C₄H₁₀); (g) and (h) 10.26 ppmv of pentane (C₅H₁₂). A column consisting of (a), (c), (e) and (g) shows spectra obtained when the gas sample was in the ARHCF, and a second column with (b), (d), (f) and (h) shows spectra retrieved with the gas sample in the MPC.

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Figure 5(a) demonstrates a zoom of the methane absorption spectrum (from Fig. 4(a)) measured in the ARHCF with a further magnified spectrum in Fig. 5(b), which presents actual data points (open circles) separated by 500 MHz. The nominal resolution of the spectrometer can be further improved with the length of delay line up to 70 MHz. It means that one can match the nominal resolution to the comb mode spacing of 125 MHz and perform measurements with resolution limited by the linewidth of individual teeth of a stabilized comb [27]. It would allow high-precision measurements of low-pressure spectra.

 

Fig. 5. (a) A zoom of the CH₄ spectrum measured in the ARHCF together with the residuum. (b) A further magnified view of one of the line features; open circles in black are measured single data points; fitted HITRAN-based spectrum is shown in red and plotted in negative for clarity.

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3.3 Detection limits

To evaluate the sensitivity of the setup, we determined the noise equivalent absorption (NEA) coefficient per spectral element given by:

The noise level in the spectra measured using the fiber-based gas absorption cell is a factor of ∼3.4 lower than in the multipass cell, which can be attributed to the higher optical power incident on the MCT detectors in the FTS. While the power transmitted through the ARHCF cell is only 2 times higher than through the MPC, we observed that with best effort alignment, the ratio of the peak-to-peak value of the centerburst of the interferograms was 3.2, corresponding well to the observed sensitivity improvement. We attribute this to the better quality of the beam after the ARHCF, which results in higher interferogram contrast. The advantage of using an ARHCF-based gas absorption cell will be even more pronounced if longer optical path lengths are required in the sensor configuration (e.g., 100 m). In such conditions, the lower transmission loss of the ARHCF will translate to a higher signal-to-noise ratio when compared to traditional MPCs.

4. Conclusions

We have presented Fourier transform spectroscopy based on an ARHCF and a mid-infrared OFC. The spectrometer is capable of measuring the absorption spectra of gases in the range between 2900 and 3100 cm⁻¹. Compared to an MPC, the ARHCF offers a similar interaction length with the sample (∼30 m) in a 1000 times lower gas sample volume (0.77 mL compared to 0.85 L). Moreover, the lower transmission loss of the ARHCF-based gas absorption cell results in 2.8 times better sensitivity than in the MPC, yielding an NEA coefficient of 8.3 × 10⁻⁸cm⁻¹Hz^−1/2 per spectral element. The existence of multiple transmission windows of the ARHCF in the infrared region opens up the possibility of measuring the same sample at different wavelengths or various gases in the same sample by tuning the comb source or using multiple comb sources. Although the gas filling time of an ARHCF is much longer than that of an MPC, research is being conducted on accessing the fiber core using a set of microchannels created by laser processing [63,64]. The fabrication of numerous access points for the gas to reach the core with simple diffusion would accelerate the filling process without adding complexity to the setup and remove the need to use the overpressure technique.

The improved sensitivity combined with the reduction of bulk-optics components required for achieving tens-of-meters-long absorption paths and the perspective of miniaturization can lead to the development of simple spectrometers capable of detecting broadband gas spectral features in low sample volumes. Such spectrometers would offer a viable alternative to comb-based PAS. The lower insertion loss of the fiber-based gas cells will be crucial for developing broadband spectrometers based on miniaturized interband cascade laser-based frequency combs, which have limited output power [65]. In addition, the stability of the ARHCF and the possibility to coil it will allow the setup to be miniaturized and have out-of-lab usage. Combining the small gas sample volume, low transmission losses and compact size of the ARHCF with the benefits of mid-infrared OFCs results in a setup capable of measuring different species of limited availability with high spectral resolution in a wide spectral range.