# A Review of Photothermal Detection Techniques for Gas Sensing Applications
## 1 Introduction
In such a case, the interferometer is constructed to have one of the measurement beams interact with the excited gas sample. The induced RI modulation will result in a change in the optical paths of one arm of the interferometer and thus produce a signal which can be easily detected. The _pump_ wavelength can be additionally modulated by a sinewave-function in the vicinity of the absorption line, causing a periodic RI modulation and can simplify the absorption signal retrieval by employing commonly used techniques e.g., wavelength modulation spectroscopy (WMS) [14; 15]. The PTS-induced RI change in the gas sample can be estimated based on Equation (1) [16]. \[\Delta n=\frac{(n-1)}{T_{0}}\ \frac{\alpha P_{exc}}{4\pi a^{2}\rho C_{p}f} \tag{1}\]  
where \(\alpha\) is the absorption coefficient of the targeted gas; \(f\) is the excitation beam modulation frequency; \(C_{p}\) is the specific heat of the gas mixture; \(\rho\) is the density of the gas mixture; \(P_{exc}\) is the _pump_ beam power, \(T_{0}\) is the absolute temperature and \(n\) is the refractive index of the gas mixture; and \(a\) is the _pump_  
Figure 1: The principle of the photothermal spectroscopy techniques. beam radius. If required, the calculated photothermal-induced RI change can be converted to a phase shift of the _probe_ beam, according to equation  
\[\Delta\varnothing=(2\pi l\Delta n)/\lambda\]  
where \(l\) is the laser-gas interaction length, and \(\lambda\) is the wavelength of the _probe_ beam. Although using multimode radiation in a Mach-Zehnder interferometer has been presented, this requires additional signal processing methods or using a bulky and expensive optical spectrum analyzer for calculating the induced phase shift. Therefore, in each of the presented PT gas spectrometers, a single mode and single frequency laser beam is used as the _probe_. From equation (1), it can be seen that the RI change and thus the resulting PTS signal is proportional to the absorption coefficient and the _pump_ laser power. On the other hand, it is inversely proportional to the _pump_ beam cross-section and the frequency of modulation. Hence, increasing the amplitude of the registered PTS signal can be conveniently achieved by utilizing a laser source capable of delivering high output powers and good beam quality (preferably with parameters M\({}^{2}\) close to 1, or with TEM00 mode for Gaussian beams, which permits tight focusing). Moreover, similarly to PAS, the PTS signal decreases with higher _pump_ laser modulation frequencies [17]. This is a direct result of the limited thermal response time of the gas molecules and has been thoroughly explained in Reference [18]. This requires fine-tuning of the _pump_ laser modulation frequency of each PTS sensor to optimize the signal-to-noise ratio (SNR), so a tradeoff between 1/\(f\) noise and registered signal is reached. Moreover, with a proper design, PTS gas sensors can have direct frequency readout of the induced RI modulation. The principle is similar to dispersion spectroscopy [19], where the gas concentration can be encoded into frequency deviation of the beat note. In such configurations, the PTS sensors represent excellent immunity to any variations of the signal amplitude. Moreover, PAS, PTS and CLADS are inherently baseline-free detection methods. If no targeted gas particles are present in the sensor, no signal is observed. This severely simplifies signal processing and limits the requirements for calibration and periodic re-adjustments of the sensor. The main aim of this work is to present several interesting and unique approaches to photothermal gas sensing. The configurations will be discussed and their performance will be compared.