# Monolithic Double Resonator for Quartz Enhanced Photoacoustic Spectroscopy
## 2 Experimental Setup  
The QEPAS spectrophone was designed to excite the QTF from the outside of the prongs. We used two off-beam mRs placed in a mirror symmetry and the QTF located in between (Figure 1). The optical path was more complex, compared to a classical off-beam QEPAS approach. The laser beam went through one microresonator (mR 1), underwent two right angle reflections that brought it parallel to the incoming beam with a lateral shift (8), and finally crossed the other microresonator (mR 2). In this configuration, one could consider two acoustic sources photogenerated with the same laser. In order to maximize the excitation of the QTF, the two acoustic sources must be in-phase. Considering two identical mRs and two identical mR-QTF gaps, the phase shift \(\Delta\varphi\) between the two acoustic sources could be calculated with the optical path difference \(\Delta L\), between the two mRs:  
\[\Delta\varphi=k\Delta L=1.3\times 10^{-5}\;\mathrm{rad} \tag{1}\]  
With \(k\) as the wave vector, \(\Delta L=2.2\) cm (\(2\mathrm{L}_{\mathrm{mR}}+\delta\) the optical path between the 2 mRs). The phase shift was negligible; therefore, the 2 mRs were considered to be acoustically in phase. The dimensions of the monolithic double mR were chosen, after the characterization of several individual mR. A set of many different mR with various dimensions, fabricated from aluminum micromachined blocks, were characterized following the setup described in [15]. We chose a large main hole (\(\mathrm{R}_{\mathrm{mR}}=0.5\) mm) to help the alignment process. The acoustic response of these individual mRs was studied using a photoacoustic signal generated by the absorption of a water line of a 1392 nm single frequency laser ([[https://eblanaphotnics.com/](https://eblanaphotnics.com/)]([https://eblanaphotnics.com/](https://eblanaphotnics.com/)) (accessed on 26 February 2021)). The laser was fully characterized, as shown in Figure 2.  
Figure 1: (**a**) Optical QEPAS setup of the double microresonator (double mR) with the 2 right angle mirrors and the QTF position. (**b**) Picture of the setup. (**c**) Picture of the complete bench, including the laser, the focusing lens, and QEPAS superophone. Figure 2: Characteristics of the EBLANA 1392 nm DFB laser. (**a**) LIV curves and (**b**) 1f-QEPAS response in an off-beam configuration with a single microresonator. The spikes at higher currents were due to insignificant experimental artefacts. The QEPAS response was obtained for a laser temperature of 28 \({}^{\circ}\)C and ambient humidity of 50% RH. The target H\({}_{2}\)O line had a line strength of 1.5 \(\times\) 10\({}^{-20}\) cm\({}^{-1}\)/(molecule \(\times\) cm\({}^{-2}\)), centered in 1392.54 nm (7181.18 cm\({}^{-1}\)). The amplitude of acoustic wave, based on a given ambient water absorption (absolute humidity \(\sim\)1% in volume ratio), corresponded to an optical absorption coefficient of 1.15 \(\times\) 10\({}^{-2}\) cm\({}^{-1}\), which was relatively high, as compared to standard gas sensor experiments, but convenient for making a proof of concept. We used a standard MEMS microphone (Knowles SPU0410 LR5H-QB) to record the frequency response of the resonators [15]. These characterizations were conducted using mRs with lengths around \(\lambda\)/2 for a 215 Hz acoustic wave, adjusted to the theoretical QTF resonant frequency. The best frequency-adjusted response was obtained for a length between 5 and 5.5 mm (Figure 3). We also fabricated 3D stereolithography printed mRs and noticed that changing the material did not modify the resonant properties--the quality factor (Q = 9 for ref a9) and the resonant frequency remained the same. Following these results, we decided to choose L\({}_{\text{mR}}\) = 5.3 mm to fit as properly as possible to the QTF resonant frequency. In this double mR configuration, the two individual mRs were uncoupled, the acoustic wave was mainly confined in the main tube.