**2. Light Guidance in Antiresonant Hollow-Core Fibers**

ARHCFs are a new type of HCFs, which light guidance mechanism can be explained by the means of the ARROW model as shown in Figure 2a. According to this, the core boundary area of the ARHCF can be treated as a Fabry–Perot resonant cavity, as it is formed by low and high refractive index layers (e.g., air and glass) as presented in Figure 2b [8]. This Fabry–Perot cavity enables only the transmission of the optical frequencies, which are not in resonance with the core wall (capillary walls). These optical frequencies are reflected back to the fiber core where they propagate with low loss. On the other hand, the resonant optical frequencies cannot be confined within the fiber core and leak away to the cladding area where they experience high leakage and material loss [8]. The antiresonant wavelength range supported by an ARHCF can be calculated according to the following formula [19]:

$$
\lambda\_{\text{antires}} = \frac{4y}{(2m+1)} \sqrt{n\_2^2 - n\_{1'}^2} \text{ } m = 0, 1, 2, \text{ } \dots \text{ } \tag{1}
$$

where *y* is the core wall thickness (capillary wall thickness), *n*1 and *n*2 are the refractive indices of the core and cladding, respectively. The resonant wavelength range can be defined as [19]:

$$
\lambda\_{\rm res} \sim \frac{2y}{m} \sqrt{n\_2^2 - n\_{1'}^2} \ m = 0, 1, 2, \dots \tag{2}
$$

**Figure 2.** Light guidance mechanism in ARHCF. (**a**) 2D representation of the ARHCF (top) showing light transmission (bottom) in the core while the coupled light wavelength is in resonance and off resonance with the core wall. When the optical frequency (wavelength) does not match the resonant frequency of the Fabry–Perot cavity, the transmission of light in the core reaches its maximum. (**b**) SEM image of the ARHCF designed to operate at ~3.4 μm wavelength with a core wall thickness of ~1 μm. The inset shows the core boundary layer forming the resonant cavity. n1 and n2—refractive indices of the air region (core, gaps between capillaries and inner parts of the capillaries) and capillary walls, respectively, x—core diameter, y—capillary wall thickness.

Based on the above equations, it can be concluded that the transmitted wavelength, and thus the position of the transmission window, depends mainly on the thickness of the capillary walls and not on the core size. However, it was reported in [29] that the hollow-core diameter of the ARHCF and diameter of the cladding capillaries have a strong impact on the bending properties and single-mode guidance of this particular fiber type. It was shown that dimensions of both have to be carefully selected to match the optimum ratio of core/capillary diameter of ~0.65 that enables single-mode transmission within the fiber low-loss window as a result of increased loss ratio between the fundamental mode and the higher-order modes supported by the fiber [8,29].

ARHCFs are fabricated with the aid of the commonly used stack-and-draw technique [30]. In majority, these fibers are drawn down from high purity fused silica glass (e.g., Suprasil F300) [8], however, due to the high material absorption of this material at the wavelengths above 5 μm, several successful attempts have been reported on fabricating ARHCFs from borosilicate and telluride glass allowing these fibers to efficiently guide light beyond the aforementioned wavelength range [28,31]. Thanks to the unique structure and light guidance properties, ARHCFs deliver better performance and versatility in comparison to other types of HCFs, especially in the area of fiber-aided gas sensing. A comparison of the parameters of the most commonly used HCFs in gas sensing is presented in Table 1.


**Table 1.** Comparison of the performance of the HCFs used in gas sensing applications.

#### **3. Tunable Diode Laser Absorption Spectroscopy**

One of the simplest and easiest methods used for laser-based gas sensing is the TDLAS [32,33]. In TDLAS, the information about the molecular concentration within a defined measurement path is retrieved based on the analysis of an interaction between the laser radiation and the gas molecules. The interaction leads to the absorption of light by the gas molecules, which are excited at the wavelength corresponding to the selected molecular transition. This phenomenon is governed by the Beer–Lambert law and expressed by the following formula [34,35]:

$$\frac{\mathbf{I}\_{\rm P}}{\mathbf{I}\_{0}} = \exp(-\boldsymbol{\varepsilon}(\lambda)\mathbf{L}),\tag{3}$$

where Ip corresponds to the light intensity after passing through the gas sample, I0 is the incident light intensity, ε represents the absorption coefficient of the gas molecules, λ is the wavelength of the light expressed in wavenumbers and L is the light-gas molecules interaction path length. In TDLAS-based gas sensors, the molecules of the target gas are typically illuminated by light delivered from a narrow linewidth laser, e.g., a distributed feedback diode laser (DFB) or a quantum cascade laser (QCL). The level of absorption of the gas molecules excitation light is observed as a drop in the signal intensity registered by a photodiode, while the laser beam is passing through the gas sample and its wavelength is tuned across the gas transition or kept at its peak. According to Equation 1, the sensitivity of the sensors relying on this method can be easily and efficiently enhanced by increasing the interaction path length within the sensor's setup. This is commonly realized by implementing bulk optics-based absorption cells or multipass cells, e.g., Herriot-, White- or toroidal-type, which are filled with the measured gas sample [12,36,37]. This approach indeed results in the improved sensor's performance, however, at the cost of the significantly increased complexity of its configuration and reduced immunity to, e.g., vibrations, temperature drifts, etc. Therefore, the application of the HCFs, especially the ARHCFs, seems to be a promising way to deliver low-volume, robust, and long optical paths. A successful demonstration of TDLAS-based gas sensors aided with ARHCFs has been already demonstrated by several research groups justifying the viability of this approach [21,24,35,38].

Nikodem et al. reported in [21] a very simple carbon dioxide (CO2) sensor configuration utilizing a silica-based 7 capillary ARHCF as depicted in Figure 3. CO2 molecules were excited using a fiber-coupled discrete mode diode laser targeting their strong ab-

sorption line at 2.004 μm. The absorption cell within the sensor setup was formed by a 1.35 m long ARHCF with a hollow core diameter of 70 μm as depicted in Figure 1a. The fiber output end facet was placed in an air-tight housing used as a gas-filling cell, which was closed with a photodetector. The light from the laser was directly coupled into the ARHCF using a simple butt-coupling method. Subsequently, the fiber-delivered beam was directed onto the photodetector using a similar approach. Hence, the sensing part of the sensor was constructed in an all-fiber configuration. The ARHCF was filled with the target gas using a slight overpressure of 100 Torr. Despite a significantly reduced sensor complexity, the proposed system was characterized by a very poor detection capability. It allowed registering clear spectroscopic signals arising from only high (at the level of 1.5%) concentrations of CO2 inside the ARHCF. This was a direct result of the high background noise level induced by the optical fringes arising from the light coupling method used, intermodal interference in the ARHCF, and its non-uniform guidance characteristic. On the other hand, the responsivity of the sensor was at the level of several seconds, which is more than two orders of magnitude faster in comparison to the detectors based on the use of conventional HC-PBGFs [39].

**Figure 3.** A schematic representation of the TDLAS/WMS gas sensor utilizing a 1.35 m long absorption cell based on an ARHCF. Reprinted with permission from [21] © The Optical Society.

Another interesting TDLAS-based gas sensor configuration shown in Figure 4 was reported by Yao et al. in [38]. The gas absorption cell in the setup was formed by a 0.85 m long ARHCF with an air-core diameter of 40 μm, which both ends were placed in air-tight gas filling cells closed with calcium fluoride (CaF2) windows. The ARHCF was filled with carbon monoxide (CO) using an overpressure of 0.8 bar, which resulted in the gas exchange time of the sensor at the level of 5 s. CO molecules inside the ARHCF core were excited with the aid of a 2.3 μm DFB laser, which was coupled into the fiber core using a set of properly selected lenses with a coupling efficiency of 90%. The minimum detection limit (MDL) in this particular sensor configuration reached 13 parts-per-million by volume (ppmv) of CO, yielding the noise equivalent absorption (NEA) of 5.2 × <sup>10</sup>−<sup>6</sup> cm−1. Similar to the earlier described work, the main limiting factor of the sensor was related to the presence of modal noise in the fiber, indicating not sufficient suppression of the higher-order modes along the relatively short fiber length and not entirely optimized light coupling conditions into the ARHCF core.

**Figure 4.** A setup of the CO sensor relying of the use of the TDLAS technique and an ARHCF-based gas absorption cell. L—lenses, M—mirror, CM—concave mirror, FM—flip mirror, P—pressure gauge, LPF—low-pass filter, PD1/PD2—photodetectors, DAQ—data acquisition card. Reprinted from [38] with permission from Elsevier.

Further work in this area reported by Yao et al. in [35] was focused on developing a TDLAS-based sensor targeting a strong transition of nitrous oxide (N2O) in the mid-IR spectral band. The sensor configuration was similar to the one presented in Figure 4, however, with the main difference in the type of the ARHCF and the used laser. In this case, the N2O molecules were excited at 2778.37 cm−<sup>1</sup> (~3.6 μm) using an interband cascade laser (ICL), which output was coupled into the gas-filled ARHCF with a coupling efficiency of 66%. The gas molecules-light interaction path was formed by a six-capillary cladding ARHCF with a core size of 65 μm and a length of 120 cm, which was filled with N2O via a pair of gas cells placed at its ends aided with an overpressure. Despite low transmission loss at the level of 0.6 dB/m at the considered wavelength, the fiber was characterized by a few-moded behavior that influenced the overall performance of the sensor. It was noticed that both the fundamental mode and the higher-order modes were simultaneously excited in the fiber, leading to the intermodal interference, which directly impacted the noise level in the registered spectroscopic signal, hence reducing the sensors' detection capability. Nevertheless, the authors have shown that this parasitic effect can be minimized by properly selecting the light coupling conditions into the ARHCF and reducing the pressure of the gas inside the fiber core. As a consequence, the sensor reached an NEA of 2.5 × <sup>10</sup>−<sup>7</sup> cm<sup>−</sup>1.

The most recent work published by Yao et al. in [24] was focused on developing a TDLAS-based gas sensor utilizing a tellurite glass-based ARHCF enabling efficient light guidance above 5 μm wavelength. The 21 cm long ARHCF consisted of six non-adjacent capillaries forming its cladding and defining the hollow core region with a diameter of 75 μm, similar to the fiber shown in Figure 1e. The input end facet of the ARHCF forming the absorption cell was placed inside a pressure-tight gas cell closed with a CaF2 wedged window, which was implemented to reduce parasitic interference. The gas cell was mechanically modified in a way that allowed it to be easily connected to the cage system rods, hence properly and efficiently align the fiber end placed in the cell with respect to the focusing lens and a QCL. This approach provided a robust and stable coupling between the laser and the fiber. Similar to the previously described work, the ARHCF was filled with the target gas using an overpressure, which allowed obtaining the response time of the sensor below 1 s. The nitric oxide (NO) molecules inside the hollow core of the fiber were pumped at 5.26 μm using a continuous wave (CW) light from a QCL. The registered TDLAS signal from 100 ppmv NO in the ARHCF was characterized by the presence of strong background noise, which resulted from the multimode nature of the fiber, and could not be eliminated by simple signal averaging or the usage of different light coupling conditions. However, the authors minimized its influence on the sensor's performance by introducing proper electrical filtering of the signal at the frequencies where the fringe noise was dominating. Thanks to this, the sensor reached an MDL of 1.2 ppmv, which corresponds to an NEA of 2.1 × <sup>10</sup>−<sup>5</sup> cm<sup>−</sup>1.
