Reliable detection of various gases is crucial for many fields, such as industrial [1] and agriculture [2] process control, environmental monitoring [3], detection of toxic compounds [4] as well as medical implementation by measurement of trace biomarkers concentration in exhaled breath [5, 6]. Therefore, it is important to develop new detection methods as well as to refine the existing ones.

Theoretically, an ideal gas sensor is characterized by a high dynamic range (preferably linear), high sensitivity that enables the detection of trace amounts of the target substance, a short response time, no need for frequent periodic calibration or component replacement, long-term stability, and the ability to operate under harsh environmental conditions. Additional advantages include compactness and the ability to work with very small gas samples. Optical gas sensors meet many of these characteristics, though rarely all simultaneously. Selecting a specific detection technique or spectral region always involves trade-offs. The simplest spectroscopic methods, such as single-pass absorption spectroscopy, are easy to implement, reliable and fast, but they offer low sensitivity. This can be increased by using e.g. modulation techniques such as wavelength modulation spectroscopy (WMS) [7]. Further improvement in sensitivity usually requires increasing the optical path over which the laser light interacts with the gas. Multi-pass cells are commonly used for this purpose [8, 9]. They can provide a significant increase in system sensitivity but require two (or more) mirrors that need to be precisely aligned. Such cells may also suffer from opto-mechanical drift [10] and the relatively large gas volume may increase measurement time. Some of the most sensitive techniques, such as cavity ring-down spectroscopy [4], cavity-enhanced spectroscopy [11], and integrated cavity output spectroscopy [12] use high-reflectivity mirrors to form high-finesse cavities that effectively extend the optical path length to several kilometers. These methods can achieve extremely high sensitivity but are complex, expensive, and require very stable alignment. Another class of sensors is devices that rely on photoacoustic spectroscopy (PAS). The most common variant of PAS is quartz-enhanced PAS, in which a quartz tuning fork (QTF) is used as an ultra-sensitive microphone [13, 14]. This approach allows for obtaining extremely low detection limits, but also requires very precise laser-QTF alignment. Moreover, QEPAS performance is highly dependent on multiple parameters (e.g. temperature, pressure inside the cell, gas flow, water vapor content), which makes frequent recalibration necessary.

Most of the measurement concepts mentioned above (especially the ultrasensitive ones) share a common limitation: complexity of the optical system. The large number of precisely aligned components makes these techniques vulnerable to mechanical disturbances and harsh environmental conditions. Consequently, there is a growing trend toward fiber-based gas-sensing setups, not only in the near-infrared but especially in the mid-infrared spectral region. A significant advancement in this direction was the development of hollow-core fibers, particularly anti-resonant fibers (ARHCFs) [15, 16].

In recent years ARHCFs have undergone rapid development, evolving from laboratory curiosities into practical optical waveguides with exceptional performance. Continuous advances in fiber design and fabrication have led to a dramatic reduction of propagation losses, reaching extremely low values in both the near-infrared and mid-infrared spectral ranges [17]. In parallel, significant progress has been made toward system-level integration, including reliable splicing of ARHCFs to conventional solid-core and hollow-core fibers [18]. Beyond sensing applications, ARHCFs have also been employed in low-latency optical data transmission [19, 20], exploiting their air-guided modes to reduce signal propagation delay, or in intense pule delivery [21, 22].

ARHCFs have also already proven to be an attractive alternative to multi-pass cells in gas sensing systems [23–26]. Conventional (i.e. solid-core) silica fibers do not support light propagation above 2.3 µm. In contrast, ARHCFs guide light through a hollow core with minimal overlap with the host material, allowing transmission in the mid-infrared [27] and giving access to the strongest molecular ro-vibrational transitions. Furthermore, the required gas volume is very small (typically less than 1 ml) even for path lengths of several meters. Moreover, their compatibility with standard fiber-optic components enables the construction of all-fiber-based gas detection systems. Such systems are robust, require no frequent realignment, and can be easily reconfigured. However, ARHCFs also exhibit two major drawbacks in gas sensing applications. The first is the presence of higher-order modes, which generate interference fringes that can exceed the amplitude of the absorption lines being measured. Fortunately, careful control of light coupling can significantly suppress these modes. The second limitation is more challenging: the hollow-core diameter, typically on the order of tens of micrometers, makes efficient gas filling difficult. Reported filling times can reach several minutes, even for relatively short fibers (a few meters long) [25, 28]. This can be mitigated by increasing the pressure differential between the fiber input and output, which drives gas flow. However, this approach is limited in effectiveness and can lead to absorption line broadening, complicating signal analysis due to spectral features overlapping each other.

The goal of this work was to design, fabricate, and test a new generation of ARHCFs with a large core (over 100 μm) that are flexible (allowing longer lengths to be coiled) and capable of single spatial mode operation in the mid-infrared. This design aims to eliminate the significant drawback of long gas-filling times while retaining all other advantages. It also accounts for technological limitations and is designed so that deviations from the ideal design parameters do not significantly affect the key parameters for measuring gas concentrations in the mid-infrared range. We present the fiber design and demonstrate its applicability to mid-infrared gas sensing. The system’s low detection limit for methane at 3.3 µm and short response time are experimentally verified.

Several assumptions were made when designing an ARHCF for this study, based not only on application requirements but also on technological limitations. Specifically, during the design phase we assumed that the gas flow inside ARHCF is laminar and isothermal, with negligible slip at the capillary walls (Re < 1000, Kn < 0.001); the gas refractive index is approximated as unity for optical modeling; the capillaries are idealized as uniform cylinders. The requirements included light propagation at 3.3 µm (where methane absorption occurs), total optical losses (propagation + bending) not higher than 1 dB m−1 and filling times of less than 10 s (for a few-meter long fiber). It is important to point out, that achieving very low losses was not the main aim of this work since only several meters of the fiber will be used for gas sensing. Additionally, an extremely broad transmission bandwidth was not crucial, as long as transmission near 3.3 µm is possible. These made the fabrication process less sensitive to imperfections such as geometric irregularities. So overall, the main objective was to develop a fiber that would combine the mid-infrared transmission with effective gas exchange, while taking into account the real limitations of the fabrication process (e.g. some variations in capillary wall thickness and diameters).

From the point of view of optical parameters, it was crucial to ensure effective single-mode propagation in the mid-infrared range (approximately 3.3 µm for methane detection). The fiber’s optical losses should be low enough to enable measurements in sections up to 10 m long, while limiting bending losses, which will allow for compact integration of the sensor into the measurement system. At the same time, the fiber structure should ensure sufficiently fast gas transport in the core so that the sensor has a response time of several seconds for pressure differences of up to a few bars. This requires a compromise between a large core surface area, which promotes gas exchange, and a limitation on the number of modes. For technological reasons, it was decided to design an optical fiber with single capillaries (i.e. not nested) arranged symmetrically inside a larger capillary forming the outer cladding. This type of geometry, while maintaining a relatively small fiber outer diameter enables a large core and good repeatability of the structure during the drawing process.

The first step in the design process was to determine the gas exchange rate in the ARHCF. Since the flow involves a compressible gas, the analysis adopted an isothermal generalization of Poiseuille–Hagen’s law for gases [29], which, under laminar flow conditions (Reynolds number Re < 1000) and continuous flow without slip on the capillary walls (Knudsen number Kn < 0.001), well describes transport in a microcapillary. The mass flow rate of gas through a capillary with length L, cross-sectional area A and hydraulic diameter Dh is given by the formula [29]:

where µ is the dynamic viscosity of the gas, p1 and p2 are the inlet and outlet pressures of the optical fiber, respectively, R and T are the gas constant and temperature, respectively, and P0 is the Poiseuille number, which accounts for the effect of the non-circular cross-section of the capillary. From the mass flow rate, the effective flushing time Tflush can be calculated, i.e. the time needed to replace the gas in a capillary with a length of L and a cross-sectional area of A [29]:

where p is the gas density at mean pressure. The value Tflush represents the convective gas exchange time. Under realistic conditions, this time may be slightly longer due to molecular diffusion and hydrodynamic dispersion, which blur the gas exchange front. Examples of Tflush gas exchange time results obtained for an optical fiber with a length of L= 10 m, an inner diameter of the large capillary of D = 140 µm, a variable number of inner capillaries N, and a variable diameter of inner capillaries d are shown in figure 1.

Figure 1. Tflush gas exchange time for a fiber with a length of L= 10 m at a pressure difference of 4 bar, depending on the number of capillaries N and the diameter of the inner capillaries d. The pink and red horizontal lines indicate exchange times of 1 and 10 s, respectively.

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The next step in the design process focused on optical properties. The 3.3 µm measurement wavelength (characteristic of methane absorption) enables the determination of the required thickness of the capillary inner walls. The anti-resonance condition was used, which determines the position of loss bands (resonances) in ARHCF, described by the relationship [30]:

where t is the thickness of the capillary wall, n is the refractive index of glass, λ is the wavelength, and m is the resonance order number, and it is assumed that the refractive index of the tested gas is equal to 1.

The analysis presented in figure 2 showed that propagation in the mid-infrared range (λ= 3.3 μm) is possible only in two regions. For thick capillaries (t > 2 µm), transmission can occur in the window between two areas of high loss corresponding to resonance m = 0 and m = 1. However, for thinner capillary walls (t < 1.5 µm) the low-loss range is limited on the shorter wavelength side by first-order resonance (m = 0) and on the longer wavelength side by increasing material losses in silica glass. Furthermore, the analysis presented in figure 2 indicates that the design is highly resistant to fabrication inaccuracies. Changes in the wall thickness (t) of the internal capillaries at the level of 10% do not significantly shift the transmission window towards resonance, which allows the fiber to operate as expected even with slight deviations during the drawing process. Therefore, taking into account the fabrication technology, application requirements, and available capillaries, thin-walled capillaries with a thickness of approximately t ≈ 1 µm were selected as the preferred solution. This design provides adequate transmission bandwidth in the mid-infrared range while maintaining structure simplicity and good fabrication tolerance.

Figure 2. Resonance positions for ARHCF fiber depending on the thickness of the inner capillary walls t. The graph shows two areas where high transmission can be achieved for a wavelength of 3.3 µm, and the longwave region where high attenuation occurs in silica glass.

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With a specific internal-capillary wall thickness, we verified how the number of capillaries and their diameter affect both the propagation (figure 3(a)) and bending losses (figure 3(b)). Both plots reveal the lowest losses for fibers containing 12 or 16 capillaries. Fibers with larger capillaries exhibit slightly lower loss. Confinement losses remain below 0.1 dB m−1, permitting reliable measurements on several-meter-long samples. Bending-loss data confirm that the fiber can be coiled into even 10 cm-radius loops without significantly increasing losses.

Figure 3. Losses in ARHCF fibers: (a) propagation losses, (b) bending losses, (c)–(g) sample designs. The second design (d) (shown with blue color) was eventually selected in our study.

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In ARHCFs, single-mode operation is primarily ensured by loss discrimination. While coupling between the fundamental and higher-order modes may occur due to bending or structural imperfections (such as surface roughness [31]), single-mode operation can be obtained if the higher-order modes experience substantially higher propagation loss [31, 32]. This is exactly the case for the designed ARHCF as the calculated propagation losses of the second mode are four times greater than those of the fundamental mode. According to simulations, the losses for the fundamental mode were 0.0188 dB m−1 and for the second-order mode 0.0782 dB m−1. Since in ARHCFs the leakage losses grow significantly with mode order [31], and with several meters long fiber, this attenuation difference should make the fiber effectively single-mode, especially when bent. This is also confirmed by our previous work [33], where we observed stable and bend-insensitive (bend radius 14 cm) propagation of a vortex beam in this fiber.

Furthermore, this fiber geometry ensures good overlap between the spatial distribution of the fundamental mode field and the gas flow velocity profile (figure 4).

Figure 4. Normalized flow velocity distribution (left) and normalized calculated light intensity in fundamental mode in the designed ARHCF.

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Taking into account the optical requirements and those related to gas exchange, a fiber with 12 capillaries and outer diameters of approximately 19 µm was selected, yielding a designed core diameter of the ARHCF to be larger than 100 µm. It is also worth noting that using a larger number of smaller capillaries is preferable to employing a smaller number of larger ones. The latter configuration would result in an ARHCF with a very large outer diameter (500–600 µm). In contrast, with the former approach (i.e. using 12 small capillaries) the outer diameter of the ARHCF can be on the order of 300 µm, which provides sufficient flexibility to allow coiling. Furthermore, drawing fibers with smaller capillaries is simpler, and the resulting fibers are less fragile when bent.

Additionally, although propagation and bending losses depend on fabrication precision—especially the circular shape of the capillaries, their size and mutual distances—the choice of a structure with 12 smaller capillaries and larger spacing between them is dictated by the desire to facilitate fabrication. This geometry minimizes the impact of fabrication errors on optical parameters, increasing the repeatability of the structure.

Figure 5 shows the SEM picture of the ARHCF. The core and outer diameters are 107 µm and 283 µm, respectively. The fiber we used in our experiments had a length of 5.2 m and could be easily coiled to a diameter of ∼20 cm. Under these conditions, we have measured the transmission losses using the cut-back technique. A supercontinuum source (SuperK MIR from NKT Photonics) and two optical spectrum analyzers (AQ6370D and AQ6376 from Yokogawa) were used to cover near- and mid-infrared from 800 to 3400 nm. Combined results from both analyzers are shown in figure 6. The ARHCF exhibits two broad transmission bands, the first from (at least) 800 nm to 1600 nm and the second from 2200 nm to (at least) 3400 nm. This is in good agreement with the simulation shown in figure 3 (blue plot that predicts no propagation from ∼1.5 to ∼2 µm). The lowest losses, approximately 1 dB m−1, occur in the mid-infrared, up to 3.4 µm. Figure 6 also shows the beam profile measured at the output of the ARHCF with an infrared-red camera (WinCamD-IR-BB from DataRay).

Figure 5. SEM picture of the ARHCF used in this work.

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Figure 6. Transmission losses of the ARHCF in the near- and mid-infrared spectral region (measured for the coiled fiber with a bend diameter of approximately 20 cm). Inset shows the beam profile measured at the output of the ARHCF with an infrared-red camera.

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To test whether ARHCF with a large core diameter is suitable for trace gas sensing with short response time, it was placed in the experimental setup schematically presented in figure 7. We used a 3.3 μm distributed feedback (DFB) interband cascade laser (ICL) from nanoplus as a source. Light from the laser was coupled into the ARHCF using a reflective collimator (RC08FC-P01 from Thorlabs). The optical fiber length was 5.2 m. It was mounted into the collimator using a temporary fiber connector (BFT1 from Thorlabs). The other end of the ARHCF was also placed into the temporary connector and mounted onto the MCT detector (PDAVJ5 from Thorlabs). Gas injection into the optical fiber was achieved using a custom made collimator housing (shown in figure 7). Reference methane cylinders (100 ppm, 24 ppm, 5 ppm) and pure nitrogen cylinder were used in the experiment.

Figure 7. Schematic diagram of the gas sensing setup (RC—reflective collimator; TC—temporary fiber connector; W—wedged window; GC—gas connection). Below shown is a picture of the collimator with gas connection.

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For the initial experiments, the laser current was modulated with a saw-tooth signal to scan the wavelength across the target methane line. Figure 8 shows the signals recorded for different gas mixtures. As the laser wavelength is tuned to the methane, the line can be recorded.

Figure 8. Target absorption line of methane for 5.2 m ARHCF filled with four gas mixtures (also visible is neighboring absorption line of water vapor).

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To further enhance measurement sensitivity, WMS method was implemented. In this case, the laser current was sinusoidally modulated at 5 kHz with an additional ramp for slow (1 Hz) wavelength scanning. The photodetector signal was demodulated using a lock-in amplifier (LIA-MVD-200-L from Femto) at the second harmonic of the modulation frequency (i.e. 10 kHz = 2 × 5 kHz). The so called 2f-WMS signal was then recorded with an oscilloscope. The most significant advantage of the 2f-WMS is that it not only suppresses noise but also removes the baseline, thereby simplifying data processing and increasing detection sensitivity. Figure 9 shows spectral scans for three gas mixtures: nitrogen, 5 ppm methane, and ambient air (which contains ∼2 ppm methane). In ambient air, four absorption lines are visible, one from methane (3270.4 nm) and three from water vapor, including a strong one near 3271.8 nm. This transition, due to very high absorption cross-section (about ∼5 times stronger than methane), is still visible after the fiber is flushed with dry gases from cylinders. This is most likely ambient water vapor (between the laser source and the ARHCF there was a short free-space section of ambient air). Furthermore, there may be a contribution from traces of water vapor still present inside ARHCF (water vapor is known to be an adhesive molecule [34]). This demonstrates the importance of analyzing naturally occurring interfering elements in the air when selecting a wavelength for detecting trace amounts of a given molecule. In this case, the lines are sufficiently spectrally separated, thus there is no overlap of spectral features. In practical application it would still be recommended to use some kind of water vapor desiccant at the gas inlet, which in combination with continuous and stable gas flow should address the issue of residual H2O inside the fiber. Additionally, the free space section of the setup should be kept as small as possible. Ideally, a laser source should be coupled to an ARHCF within a single air-tight housing filled with dry nitrogen, such as is typically done with near-infrared laser diodes. Regarding the spectra shown in figure 9, it is also important to notice that there are no visible fringes in the recorded spectra which indicates single mode propagation inside the fiber.

Figure 9. 2f-WMS signal for three different gas samples.

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To estimate the detection limit of the setup, the ARHCF was filled with ambient air, and the laser wavelength was adjusted to the center of the methane line. Ambient methane concentration was ∼2 ppm (estimated based on the measurements for nitrogen and 5 ppm methane shown in figure 9). The Allan deviation was calculated from a continuous time series of methane concentration measurements recorded for 100 s under constant conditions, using a fixed sampling interval of 1 ms. To calculate the plot presented in the paper, the time series was subdivided into non-overlapping clusters corresponding to the selected averaging times, and the Allan deviation was computed following the standard two-sample variance definition and is shown in figure 10. A detection limit of ∼4 ppb is estimated for 1 s integration time, assuming a 1σ confidence level. It could be reduced to 1.5 ppb when integration time is increased to 10 s but this averaging time already eliminates the gain from the short fiber filling time. The detection limit at a single ppb level confirms that the system has sensitivity comparable to standard arrangements based on multi-pass cells and is more than sufficiently sensitive to measure atmospheric methane variations.

Figure 10. Top: 2f-WMS amplitude measured at the line center for ARHCF filled with ambient air; bottom: Allan-Werle plot. A roll-off below 0.1 s indicates the demodulation bandwidth of the lock-in amplifier. Dashed blue line shows 1/sqrt(τ) dependence; gray lines show error bars for Allan deviation.

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The key parameter of the tested ARHCF is the rate at which it can be filled with a gas sample. To analyze the sensor response, the ARHCF was initially filled with pure nitrogen. A cylinder containing 5 ppm methane was then connected to the inlet of the ARHCF, and the 2f-WMS amplitude was recorded while the gas flowed through the fiber. The experiment was repeated for four inlet pressure values, ranging from 1 bar above ambient to 4 bar above ambient. The results (shown in figure 11) confirm a response time (defined as the time elapsed from 10% to 90% of the stable signal) on the order of seconds. While 8.8 s is obtained for a pressure difference (inlet–outlet) of 1 bar, it drops to only 4.5, 3.0 and 2.2 s when the pressure difference is 2, 3 and 4 bar, respectively. Figure 12 also shows the 2f WMS amplitude recorded when gas sample flown through the fiber was switched multiple times between methane and nitrogen. When switching cycles are overlapped (also shown) excellent reproducibility and setup stability becomes visible. Obtained filling times are also consistent with theoretical predictions (figure 13) derived from the gas-flow model introduced in section 2.

Figure 11. System response to switching from nitrogen to methane at the gas inlet for different inlet pressures. Pressure difference refers to the difference between the input and the output pressure (output pressure was kept at ambient). Note: these plots demonstrate a single gas switching event, with no data averaging.

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Figure 12. 2f WMS amplitude recorded when gas sample flown through the fiber was manually switched between methane and nitrogen. Bottom: switching cycles overlapped to show excellent reproducibility and stability of the setup.

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Figure 13. Comparison of experimentally measured T10–90 fiber filling times with theoretical predictions derived from the gas-flow model.

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It is worth noting the decrease in the signal amplitude for higher pressures which results from the broadening of the target absorption line for higher pressures (assuming quasi-linear pressure gradient along the fiber, the full-width at half-maximum of the integrated absorption line is 0.28 nm, 0.36 nm, 0.44 nm, and 0.53 nm for overpressures of 1, 2, 3, and 4 bar, respectively). The wavelength modulation amplitude was optimized for the pressure difference of 1 bar, thus for larger pressure gradients, it produced signals with reduced amplitude.

This work aimed to develop an ARHCF with a large core diameter suitable for gas sensing applications requiring short response times. Table 1 and figure 14 summarize ARHCF-based sensors reported in the literature, focusing on their response/filling times and fiber lengths, as well as detection limits. Most previously demonstrated ARHCF-based sensors employed fibers of varying lengths, ranging from less than one meter to several tens of meters. Reported filling times were on the order of a few seconds only for very short HCFs (∼1 m) [35–38]. Unfortunately, the filling time increases dramatically with fiber length, and for longer ARHCFs, values exceeding tens of seconds have been reported [25, 26, 28, 39, 40]. In contrast, the response time of only 2.2 s achieved in this work is significantly better than any previously reported value for ARHCFs. The only comparable result was presented in [41], where a 5 m-long ARHCF was filled within 6 s, roughly three times longer than the response time achieved here. Moreover, that demonstration was limited to near-infrared spectroscopy only (around 2 µm).

Figure 14. Filling time versus fiber length for ARHCF-based gas sensors reported in the literature.

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Table 1. Performance comparison of ARHCF-based gas sensors.