**4. Wavelength Modulation Spectroscopy**

WMS technique is a modification of the conventional TDLAS method, which enables reducing the influence of noise on the measured spectroscopic signal. In WMS, the wavelength of the laser that is used to excite gas molecules is (in comparison to TDLAS) additionally modulated with a sinusoidal signal with a strictly defined frequency and modulation depth, both dependent on the target gas transition characteristic [40,41]. The modulated laser frequency and the spectral absorbance in WMS are described by the following equations [41]:

$$
\boldsymbol{\omega}(\mathbf{t}) = \boldsymbol{\upodot} + \mathbf{A} \boldsymbol{\upodot}(2\pi \mathbf{f} \mathbf{t}),
\tag{4}
$$

$$-\alpha[\odot + \text{Acos}(2\pi \text{ft})] = \sum\_{\mathbf{k}=0}^{\infty} \text{H}\_{\mathbf{k}}(\odot, \text{A}) \cos(\text{k}2\pi \text{ft}),\tag{5}$$

$$\mathrm{H}\_{\mathrm{k}}(\odot,\mathrm{A}) = \frac{\mathrm{P}\_{\mathrm{X}}\mathrm{L}}{\pi} \int\_{-\pi}^{\pi} \sum\_{\mathrm{j}} \mathrm{S}\_{\mathrm{j}\,\phi\_{\mathrm{j}}}(\odot + \mathrm{A}\mathrm{cos}\,\Theta) \mathrm{cos}\,\mathrm{k}\theta \mathrm{d}\theta,\tag{6}$$

where υ(t) is the modulated laser frequency in function of time, υ¯ is the center laser frequency, A corresponds to the modulation depth, f is the modulation frequency, α is the spectral absorbance, P is the total gas pressure, Xi is the mole fraction of the absorbing gas sample, Sj is the j-th absorption line strength function and ϕ<sup>j</sup> is the j-th absorption line shape function and L defines the interaction path length. Typically, the modulation frequency is in the range of a few to a few tens of kHz with a modulation depth equal to ~2.2 × full width at half maximum (FWHM) of the selected gas absorption line. In WMS-based sensors, the sinusoidally modulated laser beam experiences a nonlinear interaction with the gas molecules. This leads to the rise of additional components in the signals registered by the photodetector at frequencies corresponding to the harmonics of the fundamental modulation frequency. The amplitude of the even harmonics is proportional to the concentration of gas molecules within the measurement path length, hence the sensitivity of such sensors can be effectively increased by elongating the gas-laser interaction path. The harmonic components can be efficiently retrieved using a phase-sensitive lock-in amplifier-based approach [20,40]. As the lock-in amplifier allows demodulation of the measured signal at the desired frequency with a limited demodulation bandwidth, the noise level, which manifests itself especially in the lower frequency range, can be reduced. Therefore, the signal-to-noise ratio (SNR) of the sensor can be significantly increased in comparison to the TDLAS-based technique, which directly enhances the detection capability of the gas spectrometers [24].

It has already been demonstrated by various research groups that a combination of the WMS technique with ARHCFs leads to a significant improvement in the sensor's detection capability, which results from the reduction of the fringe noise [21,24,38]. When the configurations of the sensors described in Section 3 of this manuscript were modified to allow WMS-based signal acquisition, the obtained NEA values were decreased by even two orders of magnitude compared to sensors operating in the pure TDLAS regime [24]. This enabled the ARHCF-based gas sensors to reach detection limits at a level comparable to the state-of-the-art bulk-optics-based setups.

Especially interesting work focused on WMS-based gas sensing aided with ARHCFs concerns the recent development of these fibers, which enabled them to guide light above 4.5 μm wavelength range. Nikodem et al. reported in [27] the first experimental demonstration of an ARHCF-based system capable of targeting a very strong N2O absorption line located at 2203.7 cm−1. As presented in Figure 5, the sensor utilized a QCL as a gas excitation source, which wavelength was tuned to the center of the selected N2O transition and subsequently coupled via an off-axis parabolic mirror into an absorption cell formed by a 3.2 m long nested ARHCF (shown in Figure 1d). The gas delivery system and method

were similar to the ones described earlier and allowed filling the fiber core within the 23 s period. The sensor in this configuration reached an MDL of 5.4 ppbv at 1 s integration time, which corresponds to a minimum fractional absorption (MFA) of 1.2 × <sup>10</sup>−<sup>4</sup> (NEA ~3.7 × <sup>10</sup>−<sup>7</sup> cm<sup>−</sup>1). The obtained detector's sensitivity was not at the record level, mainly due to the transmission characteristic of the fiber at the considered wavelength range. In this configuration, the QCL wavelength was placed at the edge of the low-loss transmission band of the fiber, where ARHCFs are typically characterized by the few-moded behavior [4]. Nevertheless, due to its unique structure, the fiber was characterized by an exceptional immunity to bending, which indicates the excellent robustness, compactness, and versatility of the ARHCF-based absorption cells delivering a few meters long interaction path.

**Figure 5.** Experimental setup of the ARHCF-based N2O sensor utilizing WMS technique and a 4.54 μm QCL. Reprinted with permission from [27]. © The Optical Society.

The operational wavelength range of the ARHCF-based gas sensors was significantly increased with the development of borosilicate-glass- and telluride-glass-based fibers [28,31], which broke the barrier of 5 μm wavelength range, where the attenuation of silica glass increases rapidly [3,42]. Thanks to this unique feature, the ARHCF technology could be implemented in NO detectors. Jaworski et al. reported in [20] the first experimental demonstration of a WMS-based NO sensor utilizing a 1.15 m long borosilicate glass ARHCF, as depicted in Figure 6a. The sensor targeted a strong NO doublet located in the vicinity of 1900.08 cm−1, which was registered with the aid of a QCL. The gas filling method was similar to the one described earlier. Thanks to the large core size of the ARHCF (122 μm diameter), the sensor was characterized by the filling time of less than 10 s as shown in Figure 6b. As a result of the low-loss and single-transversal-mode guidance of the fiber, the sensor reached an MDL of 20 parts-per-billion by volume (ppbv) for 70 s integration time, which yields an NEA of 2.0 × <sup>10</sup>−<sup>5</sup> cm−<sup>1</sup> and allowed registering clear spectra of 2f WMS signals from 100 ppmv NO inside the fiber as plotted in Figure 6c. Figure 6d shows a photograph of the sensor, which length does not exceed 75 cm. It is expected that the size of the sensor could be further reduced by decreasing the size of the electronic and optomechanical components used together with tightened bending of the fiber-forming the absorption cell. The authors indicated that the obtained MDL was less than an order of magnitude worse in comparison to a sensor utilizing the more advanced and complex quartz enhanced PAS technique [43]. This result was further improved by Yao et al. as reported in [24], where the WMS-operating sensor utilizing a tellurite ARHCF reached an MDL of 6 ppbv for 30 s integration time.

**Figure 6.** NO sensor operating at 5.26 μm based on the use of the WMS technique and a borosilicate ARHCF. (**a**) Experimental setup. QCL—quantum cascade laser, LDTC—laser driver, FL—focusing lens, FG—function generator, ATH— air tight housing, MCT—mercury-cadmium-telluride photodetector, PG—pressure gauge, VP—vacuum pump, LIA—lock-in amplifier, DAC—data acquisition card, PC—computer. (**b**) Gas filling profile of the ARHCF using an overpressure-assisted gas delivery method. (**c**) 2f WMS signal spectrum of the NO doublet for 100 ppmv NO inside 1.15 m ARHCF. Reprinted with permission from [20] © The Optical Society. (**d**) Photograph of the sensor setup.

> Another interesting and highly advantageous feature of the ARHCFs concerns their unique ability to transmit with low-loss light in several dissimilar wavelength bands. Jaworski et al. utilized this phenomenon for gas sensing and for the first time demonstrated the simultaneous detection of CO2 and methane (CH4) inside the ARHCF, targeting the transitions of these gases in the near- and mid-IR spectral bands [8]. The experimental setup shown in Figure 7 consisted of a difference frequency generation (DFG) and DFB sources, which operated at 3.334 μm and 1.574 μm, respectively. The DFG source was used to excite molecules of CH4, while the DFB laser targeted the CO2 transition. Both lasers were simultaneously coupled into a 1 m long ARHCF (shown in Figure 1c) filled with a mixture of the aforementioned gases through a gas filling cell. Thanks to the low loss and near single-mode guidance of the fiber at both wavelengths, the sensor reached an MDL of 24 ppbv for 40 s integration time and 144 ppmv for 1.5 s integration time for CH4 and CO2, respectively. The obtained MDLs yielded NEA coefficients of 1.6 × <sup>10</sup>−<sup>7</sup> cm−<sup>1</sup> (CH4) and 1.17 × <sup>10</sup>−<sup>7</sup> cm−<sup>1</sup> (CO2). The sensitivity of the sensor beats the performance of the WMS-based setups utilizing Kagome HCFs and HC-PBGFs, confirming the versatility of this approach [14,18]. The authors indicated that the further improvement of the developed sensor's sensitivity could be obtained by introducing a longer fiber (i.e., with several tens of

meters in length) with a properly modified structure, allowing obtaining pure single-mode transmission and uniform loss within the guidance windows.

**Figure 7.** Schematic of the dual-gas sensor based on the near- and mid-IR guiding ARHCF and WMS technique. SSL—diode pumped solid state laser, FC—fiber collimator, ISO—isolator, YDFA/EDFA—Ytterbium- and Erbium-doped fiber amplifiers, L—lenses, M—mirror, DM—dichroic mirror, G—germanium window, W—CaF2 wedge, FG—function generator, LIA—lock-in amplifier, DAC—data acquisition card, PC—computer, VP—vacuum pump. Reprinted from [8] with permission from MDPI.
