## 1 Introduction  
Photothermal spectroscopy (PTS) and photoacoustic spectroscopy (PAS) are well-established methods for experimental physics, chemistry, and biology. The history, processes, and application of PTS and PAS in gas phase analysis have previously been discussed in detail [1; 2; 3]. The photothermal and the photoacoustic effects can be divided into three stages: (1) release of heat due to the vibration-translation relaxation of molecules upon absorption of laser radiation; (2) generation of thermal and acoustic waves due to periodically heating and expansion; (3) collection and amplification of thermal and acoustic signals. According to the laws of fluid mechanics and thermodynamics, the laser-induced thermal and acoustic wave pressure \(p\) in a gas can be determined by Equation (1) [3]:  
\[\partial_{t}^{2}p(\mathbf{r},t)-c^{2}\
abla^{2}p(\mathbf{r},t)=(\sigma-1)\partial_{t}H (\mathbf{r},t), \tag{1}\]where \(c\), \(\sigma\), and \(H\) are the sound velocity, the adiabatic coefficient of the gas, and the heat density deposited in the gas, respectively. Equation (1) has two independent solutions: Weakly damped acoustic waves with the wavelength of approximately a few centimeters and heavily damped thermal waves with the waves of approximately a few hundred micrometers [3]. The acoustic waves propagated a few centimeters and accumulated in the PAS cells. However, the thermal waves can only be detected in the vicinity of the laser beam. Usually, PAS and PTS are studied independently since the thermal and acoustic waves are separated in space. Photoacoustic spectroscopy is an optical detection method widely used for trace gas analysis. Transducers such as microphones [4; 5; 6], cantilevers [7; 8; 9; 10], or piezoelectric elements [11; 12; 13] were used to detect acoustic waves and convert them into mechanical or electrical signals. As a significant variant of PAS, quartz-enhanced photoacoustic spectroscopy (QEPAS) has been boomingly developed in the past decades [14; 15]. In QEPAS, a quartz tuning fork (QTF) with a specific resonance frequency of \(\sim\)32 kHz and an extremely high Q factor value of \(\sim\)10, 000 was used to collect the acoustic waves and accumulate the acoustic energy [16; 17; 18]. Because of the high resonance frequency of \(>\)10 kHz, the narrow resonance spectra of \(\sim\)4 Hz, and the quadrupole electrode pattern of the QTF, QEPAS is immune to the background acoustic noise which results in a high detection signal-to-noise ratio and sensitivity [15]. The gas sensor based on the QEPAS technique has been applied for chemical analysis [19; 20; 21; 22], atmospheric monitoring [23; 24; 25; 26; 27], and biological diagnostics [28; 29; 30]. As with photoacoustic spectroscopy, photothermal spectroscopy is an indirect method for measuring the change in the thermal states of the sample that is induced by the absorption of laser radiation. Examples of photothermal techniques include photothermal interferometry (PTI), photothermal lensing (PTL), and photothermal deflection (PTD). With the merits of zero-reference and laser power dependence, photothermal spectroscopy is highly sensitive. Traditional thermally sensitive transducers include pyroelectric crystals, bolometers, and microelectromechanical systems (MEMS). Most recently, a highly sensitive PTS technology called quartz-tuning-fork enhanced photothermal spectroscopy (QEPTS) was developed for trace gas analysis by use of a QTF [31]. A QTF was used as the high-performance transducer to convert the photothermal signals to electrical signals. The laser beam passed through a 20 cm-long gas-sampling cell and then was focused on the QTF prong. The heat released by the target molecules upon absorption of the laser radiation was collected by the QTF. The heat expansion drove the QTF to vibrate. Then the resonance of the QTF amplified the signal. In QEPAS, the laser beam must be collimated to pass through the spacing of \(\sim\)300 \(\upmu\)m without touching the QTF prongs.