*5.4. PABS in ARHCF*

PAS is a spectroscopic technique similar to the PTS, however, in this case, the modulation of the phase of the *probe* light along the gas-molecules interaction path length results from an increase of the local pressure gradient due to gas molecules excitation by the *pump* laser light [57]. When the *pump* laser beam intensity is additionally modulated at a certain frequency, the pressure will change periodically, producing an acoustic wave having a frequency equal to the modulation frequency of the *pump* light [57]. The photoacoustic effect has been widely used in laser-based spectroscopy, delivering an exceptional sensitivity of the PAS-based gas sensors [58–60].

The PAS technique was recently combined with gas sensing inside an ARHCF by Zhao et al. in [23]. The authors have shown that it is possible to efficiently excite acoustic modes inside the gas-filled fiber core as a result of the photoacoustic effect and the structure of the ARHCF. This modulates the RI of the gas sample and subsequently the phase of the *probe* beam in the fiber. The interaction between the optical and acoustic modes is explained by means of the Forward Brillouin Scattering (FBS) phenomenon [61]. The silica cladding of the ARHCF forms an acoustic resonator and the gas-filled part of the fiber acts as a region for acoustic wave generation. As a result, the modulated light-excited and heated gas molecules induce an acoustic wave, which is resonantly enhanced inside the ARHCF. When the *probe* light propagates inside the fiber, it experiences a phase modulation, which can be measured using the earlier described dual-mode interferometer method. Since an ARHCF supports capillary and core acoustics modes as shown in Figure 13a,b, the optical LP01 and LP11 modes differently overlap with them, which introduces different phase

modulation of each of these modes. The observed differential phase modulation can be described by the following formula [23]:

$$
\Delta\mathcal{Q}(\Omega\lambda\_{\mathbb{P}}) = \xi(\Omega)\mathfrak{a}(\lambda\_{\mathbb{P}})\mathrm{CL}\_{\text{eff}}\mathrm{P}\_{\mathbb{P}'} \tag{12}
$$

where Ω is the modulation frequency, λ<sup>p</sup> is the *pump* wavelength, ξ defines the normalized phase modulation coefficient, α is the absorption coefficient, C is the gas concentration in the ARHCF, Leff is the effective length of the ARHCF (directly depending on the molecular concentration, absorption coefficient and the actual fiber length), and Pp is the *pump* power. The gas sensing using PABS in the ARHCF was experimentally verified in the setup depicted in Figure 13c. A DFB laser operating at 1532.83 nm was used as the *pump* source for C2H2 molecules excitation in a 30 cm long ARHCF-based absorption cell. The *pump* light was modulated with a sinewave signal at the frequency Ω, which corresponds to the frequency of the selected acoustic mode with the aid of an acousto-optic modulator (AOM). The *probe* beam was delivered from an ECDL and simultaneously coupled with the *pump* beam into the gas-filled ARHCF. Via the lateral offset coupling to the ARHCF, it was possible to excite LP01 and LP11 modes, hence forming a dual-mode interferometer. The ARHCF was filled with the measured gas via a gas filling cell. The optical signal was directed to a balanced photodetector to minimize the intensity noise and subsequently demodulated at f = Ω/2π using a lock-in amplifier. The system was characterized to provide an MDL of 8 ppbv for 100 s integration time. Operation of the system at frequencies in the range of MHz allows it to minimize the negative influence of the 1/f noise, which is not obtainable in PTS-based gas sensors.

**Figure 13.** (**a**) A capillary acoustic mode in the ARHCF. (**b**) A core acoustic mode in the ARHCF. fc is the eigenfrequency of each mode. (**c**) Experimental setup of the PABS sensor. DFB—distributed feedback diode laser, ECDL—external cavity diode laser, PC—polarization controller, AOM—acousto-optic modulator, f is the sinewave modulation frequency generator, EDFA—erbium-doped fiber amplifier, BPF—optical bandpass filter, WDM—wavelength division multiplexer, PD—photodetector, BPD—balanced photodetector. Reprinted with permission from [23] © The Optical Society.
