**5. Photothermal and Photoacoustic Spectroscopy**

PTS is a technique where the spectroscopic signal retrieval is directly related to the heating of gas molecules with the aid of laser light [44,45]. In PTS, the gas molecules are excited with a laser source (*pump*) that emits radiation at a wavelength matching the selected gas transition (similarly to TDLAS and WMS). However, the retrieved signal is not connected with the intensity drop of the laser due to its gas-induced absorption, but with the local refractive index (RI) change that results from the increased temperature of the gas sample due to non-radiative relaxation of the molecules illuminated by the *pump* light [44]. The observed change of the RI can be determined based on the following equation [46]:

$$
\Delta \mathbf{n} = \frac{(\mathbf{n} - 1)\varepsilon \mathbf{P\_{exc}}}{\mathbf{T\_0} 4\pi \mathbf{a}^2 \rho \mathbf{C\_p} \mathbf{f}} \,\mathrm{'}\tag{7}
$$

where n and ε are the refractive index and absorption coefficient of the gas sample, respectively, Pexc is the intensity of the *pump* light, T0 is the absolute temperature, a is the *pump* beam diameter, ρ is the gas sample density, Cp corresponds to the specific heat of the gas sample, f is the modulation frequency of the *pump* light. The photothermal-induced RI change is typically retrieved using the second laser—*probe* (with a wavelength different from the *pump* light), usually using an interferometric approach. The *probe* light due to RI change experiences a phase shift according to the following formula [44]:

$$
\Delta \varphi = \frac{(2\pi \text{L} \Delta \text{n})}{\lambda},
\tag{8}
$$

where L is the laser-gas molecules' interaction path length and λ is the wavelength of the *probe* light. The unique feature of the PTS is the fact that the *probe* beam wavelength can significantly differ from the *pump* wavelength, hence the PTS signal readout can be achieved using inexpensive and widely available electronic, fiber, and optical components developed for the so-called telecom spectral band (i.e., ~1.55 μm). In addition, when the *pump* light is modulated with a sinewave signal, the spectroscopic information can

be conveniently retrieved using the WMS-based technique [47–49]. Furthermore, the RI modulation can be also encoded into the frequency deviation of the beat note of the *probe* beam by using the heterodyne detection [49]. In such a configuration, the signal analysis in the frequency, not amplitude domain gives the PTS sensors immunity to the negative influence of, e.g., optical fringes, which results in the baseline-free signal retrieval, hence very high sensor sensitivity. It can be seen from the aforementioned equations that the PTS signal can be linearly enhanced with the increase in the *pump* power density over the interaction path length, however, a perfect overlap between the *pump* and the *probe* beams is mandatory, but not simple to achieve using bulk optics-based components. The perfect solution to this problem comes with the aid of ARHCFs. These fibers are characterized with mode field diameters (MFD) typically in the range of a few tens of micrometers, which means that a small beam size, hence high power density can be efficiently confined and maintained throughout the entire fiber length. Furthermore, the ability to guide light in dissimilar wavelength regions allows ARHCFs to transmit simultaneously both the *pump* and *probe* light in the gas-filled core, providing the perfect overlap between them. So far, several configurations of the PTS sensors utilizing ARHCFs as absorption cells have been developed based on the Mach-Zehnder (MZI) and Fabry–Perot (FPI) interferometer setups and shown to provide an exceptional detection capability [22,26,50–54].
