*5.2. FPI PTS in ARHCF*

Another approach to measuring the photothermal effect refers to the application of an FPI, which enables efficient detection of the phase change of the propagating *probe* beam after passing through the heated gas sample, hence experiencing the locally modulated RI. The intensity of the beam exiting the Fabry–Perot cavity can be determined based on the equation [44,56]:

$$\mathcal{I}\_{\rm t} = \mathcal{I}\_0 \frac{1}{1 + \left(\frac{2\mathcal{F}}{\pi}\right)^2 \sin^2\left(\frac{\Delta\varphi}{2}\right)},\tag{9}$$

where It is the transmitted beam intensity, I0 is the intensity of the beam before entering the Fabry–Perot cavity, F is the cavity finesse, Δϕ corresponds to the phase change, which can be further defined by [44]:

$$
\Delta\varphi = \frac{2\pi}{\lambda\_{\text{P}}} 2\text{nL}\cos\theta\_{\text{\textdegree}} \tag{10}
$$

where λ<sup>p</sup> is the probe laser wavelength, n is the RI, L is the cavity length, and cosθ defines the angle of incidence. It can be seen that due to the photothermal effect inside the cavity, the modulation of the RI has a direct impact on the change in the intensity of the transmitted radiation, which combined with the PTS effect can be used to determine the molecular concertation of the measured sample. Furthermore, in comparison to the homodyne MZI PTS detection scheme, the FPI PTS sensor can achieve long-term repeatability via a noncomplex stabilization of the *probe* laser wavelength to the quadrature of the FPI using a proportional-derivative-integral (PID) based approach [52]. Several configurations of the FPI PTS sensors utilizing the ARHCFs have already been demonstrated and will be discussed in this subsection.

Chen et al. reported in [26] an FPI PTS gas sensor targeting ethane (C2H6) at 3.348 μm, which setup is presented in Figure 9a. The absorption cell was formed by a 14 cm long HC-NCF with a core diameter of 65 μm. The molecules of the target gas were excited using an ICL operating at the aforementioned wavelength, while the *probe* beam was delivered from a 1.55 μm fiber laser. The FPI cavity layout is shown in Figure 9b. The *probe* light was coupled into the HC-NCF directly from a conventional single-mode fiber (SMF) using a butt-coupling approach. The same technique was used to couple the *pump* light, however, the ICL beam delivery fiber was an InF3 (indium fluoride) mid-IR guiding SMF. The FPI cavity was realized based on the ~4% probe light reflections at the HC-NCF/SMF and HC-NCF/InF3 SMF interfaces. The end facets of each fiber were glued into the ceramic ferrules, which mechanically stabilized the coupling between them and were used to deliver the gas sample into the HC-NCF core. The *probe* laser wavelength was locked and stabilized at the quadrature point of the interference fringe using a servo loop, which allowed converting the induced phase change into the intensity change at the output of the FPI. The *pump* wavelength was additionally modulated with a sinewave signal to perform WMS-based signal readout at the 2nd harmonic of the modulation frequency. The remaining *pump* light leaving the HC-NCF was filtered out by the 1.55 μm SMF. The stabilization was mandatory to obtain efficient operation of the sensor and its long-term stability, which was experimentally verified by registering the 2f signal amplitude over an 8 hour period. The system allowed obtaining an MDL of 2.6 ppbv for 410 s integration time, which gives an NEA of 2.0 × <sup>10</sup>−<sup>6</sup> cm<sup>−</sup>1.

Krzempek et al. presented in [52] an FPI PTS sensor configuration aided with a borosilicate ARHCF (shown in Figure 1f), which pushed for the first time the operational wavelength of such sensors beyond the 5 μm range. The experimental setup of the sensor is shown in Figure 10a. In this configuration, the *pump* light was delivered from a QCL operating at 1900.09 cm−1, which provided access to a strong transition of NO. The *probe* beam came from a standard telecom DFB laser delivering 1.55 μm output. The *probe* laser wavelength was stabilized using the PID-based approach to keep it operating at the quadrature point of the FPI. The 1550 nm light after passing the circulator was coupled into the ARHCF using the butt coupling technique. After leaving the ARHCF, the *probe* beam was reflected back to the fiber from a germanium window and directed via the circulator to the near-IR photodetector, which combined with a lock-in amplifier allowed 2f WMS-based signal readout. The FPI cavity in the sensor was formed by the *probe* beam reflections from the SMF28 end facet (R1) and the germanium window (R2) as depicted in Figure 10b. The absorption cell was constructed based on a 25 cm long ARHCF with a core size of 122 μm. The ARHCF was filled with the target gas mixture through a set of femtosecond laser processed microchannels, which provided direct access to the core region and eliminated the need of using gas filling cells. The fiber was glued into a steel tube equipped with a gas delivery port, which enabled the authors to efficiently fill the fiber with NO. The

registered 2f signal spectrum shown in Figure 10c perfectly matches the simulated signal and confirms the baseline-free characteristic of the sensor. The unique sensor configuration combined with the ARHCF ability to simultaneously guide near- and mid-IR light resulted in an MDL of 11 ppbv for 144 s (NEA ~1.68 × <sup>10</sup>−<sup>7</sup> cm<sup>−</sup>1) integration time with an NNEA of 4.29 × <sup>10</sup>−<sup>7</sup> cm−<sup>1</sup> WHz<sup>−</sup>1/2.

**Figure 9.** FPI PTS C2H6 gas sensor based on the use of a mid-IR ARHCF. (**a**) Experimental setup. PC—polarization controller, OC—circulator, ICL—interband cascade laser, FG—function generator, DAQ—data acquisition card, PD—photodetector, LPF—low-pass filter, SMF—single-mode fiber, HC-NCF—hollow core negative curvature fiber. (**b**) The absorption cell is formed by the gas-filled HC-NCF (ARHCF), which is butt-coupled with a conventional SMF and mid-IR SMF. R1 and R2 indicate the reflections in the FPI cavity formed by the interfaces between the coupling points of these fibers. Reprinted with permission from [26] © The Optical Society.

**Figure 10.** FPI PTS NO sensor utilizing a borosilicate ARHCF. (**a**) Schematic of the sensor setup. LDTC—laser driver, MIX—frequency mixer, FG—function generator, LIA—lock-in amplifier, DET—photodetector, PID—proportional-derivativeintegral controller, CIR—circulator, G—germanium window, FL—focusing lens, QCL—quantum cascade laser, VP—vacuum pump, PG—pressure gauge. (**b**) FPI cavity (top). R1 and R2—reflections in the FPI, M1, and M2—FPI mirrors. 25 cm long ARHCF-based absorption cell (bottom) glued into a steel tube inserted into a gas delivery t-junction port. (**c**) Registered 2f signal spectrum from 300 ppmv NO in the ARHCF (black trace) and simulated (red trace). Reprinted from [52] with permission from Elsevier.

FPI PTS sensor aided with ARHCFs was also designed and developed to operate only in the near-IR spectral band, where both the *pump* and the *probe* beam were transmitted within the same low-loss window of the ARHCF. Bao et al. reported in [54] an acetylene (C2H2) sensor that utilized a 5.5 cm long ARHCF that was *pumped* with 1532.5 nm using a DFB laser. The FPI cavity was similar to the one shown in Figure 9b. The *probe* light at 1551.3 nm was provided by the external cavity diode laser (ECDL) and was separated from the unabsorbed *pump* light in the gas-filled ARHCF using a wavelength division multiplexer (WDM) before being directed onto a photodetector and further analyzed. The spectroscopic signal retrieval was realized using the same approach as described above. The sensor reached an MDL of 2.3 ppbv for 670 s integration time and an NEA of 2.3 × <sup>10</sup>−<sup>9</sup> cm<sup>−</sup>1.
