Quartz crystal tuning fork- (QCTF) based light detector

Before gas detection experiments, the resonant frequency of the QCTF detector is first simulated by establishing a physical model combing using the COMSOL finite element analysis method. The establishment of the QCTF resonant model includes the setting of tuning fork geometric parameters and material parameters. The QCTF fork arm simulated in this experiment is 3.7 mm long and 0.6 mm wide. The entire physical dimensions of the QCTF are 6 mm long, 1.5 mm wide and 0.3 mm thick. The QCTF physical diagram is shown in Figure 3. For theoretical simulation using finite element analysis, the simple mechanical model of the QCTF is established as shown in Figure 4. The main component of the material is SiO₂; an elastic modulus of 70 Gpa, a Poisson’s ratio of 0.17 and a density of 2300 kg × m⁻³ are used for calculation. The established QCTF model has a good symmetrical structure and reasonable parameter settings, which makes the established model very close to the experimental conditions.

In the theoretical simulation, the COMSOL finite element method is used to decompose a series of continuous solution domains into multiple groups of discrete small regions, and the approximate function is used in each small region to represent the unknown field function for solving for the solution domain. The approximate function is generally expressed using the numerical interpolation function of the original unknown field function and its derivatives at each node in a small region. By changing a series of continuous, infinite degrees of freedom problems into a discrete, finite degree of freedom problems, the whole simulation process can be implemented quickly. When simulating the resonant frequency of the QCTF, we found that the vibration models of the QCTF can be divided into symmetrical vibrations and asymmetric vibrations [10], and only the symmetrical vibration model is the effective model for producing the piezoelectric effect; thus, the symmetrical vibration model is investigated in detail. Through the COMSOL finite element analysis of the first six resonant models of the QCTF, it is found that the fourth-order resonant model is the symmetrical vibration; the fork arm of the QCTF first moves outward and then inward, as shown in Figure 5. For this resonant model, the calculated resonant frequency is about 32,406 Hz.

After the theoretical simulation, the resonant frequency response characteristics of the QCTF were further investigated experimentally to better understand their photoelectric conversion efficiency. As described above, the QCTF-based photoelectric detector was used for collecting laser beams by employing its resonant effect and piezoelectric effect. The laser signal of the QCTF was first recorded in the time domain, and then its frequency spectrum was calculated using a self-developed fast Fourier transform (FFT) algorithm, and the peak value of frequency spectrum was finally extracted as the signal amplitude. For example, the QCTF signal-processing procedure is demonstrated in Figure 6. According to this signal-processing procedure, the experimentally measured resonant profile of the QCTF detector is shown in Figure 7, and a Lorentzian line-shape mode was used to fit the experimental data. The analysis indicated that the QCTF used in this work had a resonant frequency of 32,753.4 Hz in ambient air and a quality factor Q-value of 6468.65.

To further evaluate the gas sensor system, sulfur hexafluoride gas was used for the relevant experiments. Various sulfur hexafluoride samples with different concentrations were prepared for experimental tests. The whole experiment was carried out at room temperature and at a standard atmospheric pressure. At the beginning of the experiment, the gas sample cell was extracted to a vacuum environment to record the background signal for signal normalization processing analysis. Then, the sulfur hexafluoride sample was filled and diluted for signal spectra. In this study, the ECQCL laser emitted from 1130 cm⁻¹ to 1440 cm⁻¹, with a step frequency of 1 cm⁻¹/s. Experimental data were synchronously collected with an approximate 1 Hz sampling rate. To improve the spectral signal-to-noise ratio (SNR), the repetition rate of the ECQCL was set to match the QCTF resonance frequency (i.e., 32,753.4 Hz) as closely as possible, so as to achieve the maximum output power. According to the parameters mentioned above, it takes about 310 s to finish the whole wavelength tuning scan. Figure 8 (upper panel) shows the absorption spectra of sulfur hexafluoride gas under different concentrations. By comparing this to the reference spectrum in the NIST database as shown in Figure 1, the experimental data indicate that two distinct absorption bands of sulfur hexafluoride near 1257 cm⁻¹ and 1390 cm⁻¹, respectively, have been confirmed. However, a weak absorption peak near 1355 cm⁻¹ is not found in the experimental data. Note that this weak absorption peak near 1355 cm⁻¹ is also not found in a previous publication reported by Chapados et al. [11]. Moreover, the sensor system characteristic of concentration response was also evaluated by selecting the absorption peaks at 1257 cm⁻¹ and 1390 cm⁻¹, respectively, as shown in Figure 8 (bottom panel). A linear regression algorithm was used to analyze the experimental data. As the theory predicted, a good linear dependence of the absorption signal at 1257 cm⁻¹ and 1390 cm⁻¹ on SF₆ concentration was obtained, with a regression coefficient R² of 0.9997 and 0.99264, respectively. The results indicate that the ECQCL gas sensor system is proportional to the concentration of the absorbing molecule, and the calibration curve can be used for determining the gas concentration of an unknown sample.

To evaluate the stability and the sensitivity of this system, the Allan–Werle deviation analysis was used for experimental data [12,13]. It was conducted on the continuous measurement of spectral signal at 1257 cm⁻¹, as shown in Figure 9a. The Allan–Werle deviation plot presented in Figure 9b indicates that the sensitivity of the developed SF₆ gas sensor system is 1.89 ppm at 1 s averaging time and the measurement sensitivity can be improved to 0.38 ppm with an averaging time of 131 s.