# Monolithic Double Resonator for Quartz Enhanced Photoacoustic Spectroscopy
## 2 Experimental Setup
Its amplitude quickly decreased out of the T tube, as can be seen in Figure 4. To evaluate the normalized sound distribution inside and outside the mRs, a thermo-acoustic frequency analysis of the pressure wave was realized by the finite element method (COMSOL). As predicted by analytical approaches [10; 15], the wave was not entirely confined into the tube--about 30% of the total pressure extended outside due to the open ends effect and because of the T-shape. The two mRs were accurately pre-positioned thanks to the monolithic design. They were spaced with a distance equal to the width of the QTF, plus an ideal gap of 70 \(\upmu\)m on each side [15]. The two mirrors were glued onto a plate, thus setting an angle of 90\({}^{\circ}\) between the two reflective surfaces. The back plate slid along a shoulder in the back of the holder. Therefore, the two mirrors could be translated in the x direction, offering a simple mean of adjusting the distance between the in/out beams. Figure 3: (**a**) Sectional view and dimensions of 3 mRs a7, a8, and a9, sharing the same radius and different length. \(\tau_{0}\) = 0.25 mm, \(\tau_{0}\) = 0.3 mm. (**b**) Normalized experimental acoustic resonance of the 3 resonators. The setup was pre-aligned using a red laser. The visible laser was positioned instead of the IR laser and sent to mR 1. The mirrors were translated until the exiting beam consistently crossed mR 2. Next, the red laser was replaced by the IR laser and a focusing lens (f = 4 mm, Thorlabs C036 TME-D). A power meter was used to monitor the output power. The exiting beam was sent to the power meter by using a tiny flat mirror, without cutting the incoming beam. The beam had to cross the 2 mRs without impinging their wall, meaning the beam size width had to be smaller than the mR radius over a distance \(\Delta L\) equal to 2.2 cm. The laser was positioned about 20 cm far from the spectrophone to obtain a slowly converging beam. Using Gaussian optics and considering a beam waist of 1 \(\mu\)m at the laser output and the given lens, it could be shown that the laser beam could cross the double mR without any reflection. Approximately half of the initial optical power was measured at the output. This value could be mainly explained by the contribution of direct absorption by ambient water vapor (for a path length of 25 cm, and 50% RH, the power loss reached 36%). The remaining losses could come from reflections on the aluminum mirrors. An xyz translation stage was used to accurately position the QTF in between the mRs. The QTF resonance was measured by means of electronic excitation and used as a control signal during the descent inside the monolithic double mR setup. This continuous control technique was necessary to prevent the QTF collision and breakage. The frequency responses of the QTF, free and inside the mR, were compared, showing a Q factor of 14,140 and 9300, respectively (Figure 5). The Q value decrease (of about 30%) in this configuration was similar to the off-beam one. It was mainly due to the acoustic coupling between the QTF and mR [11]. The large signal offset observed in the characterization was due to the parallel capacitance of the coaxial cable connecting the transimpedance amplifier and could be easily suppressed. The parasitic capacitance could be suppressed by placing the amplifier closer to the QTF. Figure 4: (**a**) Detailed dimensions of the monolithic double mR. The laser beam is represented in red. It is reflected by the right angle mirrors. (**b**) Normalized acoustic pressure generated into the double mR for f = 32,815 Hz, corresponding to the QTF resonant frequency. The Q factor was determined through the curve fitting with the Butterworth Von Dyke model.