Trace gas detection is crucial in various fields, including environmental monitoring, transformer fault inspection, and medical diagnostics^[1-9]. Non-spectroscopic detection techniques, such as gas chromatography and mass spectrometry, are widely used due to their simplicity and broad applicability. However, these methods are inherently invasive and limited to offline measurements. In contrast, spectroscopic detection techniques overcome these limitations. Among them, absorption spectroscopy offers high detection sensitivity and rapid response^[10-15]. Additionally, the unique fingerprint characteristics of gas molecules in laser absorption provide excellent selectivity, making this technology highly effective.

As an important branch of absorption spectroscopy, photoacoustic spectroscopy (PAS) based on the photoacoustic effect has been the focus of trace gas detection^[16-23]. In PAS, a photoacoustic cell (PAC) is a place where the photoacoustic effect occurs, which has an important impact on the sensor performance. At present, various types of resonant PACs have been reported, such as T-type PAC^[24-26], H-type PAC^[27,28], spherical PAC^[29-31], and variants^[32-34]. The resonant structure exhibits high detection sensitivity due to resonant amplification. However, the drift of the resonant frequency in complex application environments will cause the photoacoustic signal to be unstable. In contrast, the non-resonant PAC offers the significant advantage of a simplified design that eliminates the need to account for the relationship between acoustic modes and resonant frequencies^[35-37]. This design flexibility allows for operation without requiring specific frequency matching. Moreover, the sound pressure signal in the non-resonant PAC is nearly uniform^[38], so the position of the detector can be arbitrarily chosen, which is extremely suitable for narrow spaces.

A quartz tuning fork (QTF) has a small size and low cost, and its high quality factor (Q) can effectively avoid the interference of low-frequency environmental noise^[39-46]. Therefore, the modification of the traditional microphone-based PAS, quartz-enhanced photoacoustic spectroscopy (QEPAS), was first proposed in 2002^[47]. QEPAS uses a QTF instead of a traditional microphone as an acoustic wave transducer for the photoacoustic signal, realizing the miniaturization of the detection system and the enhancement of noise resistance^[48-54].

This study presents a non-resonant quartz-enhanced photoacoustic spectroscopy (NR-QEPAS) sensor for the first time, to the best of our knowledge. In this sensor, the sound pressure remained nearly uniform throughout, eliminating the need for precise positioning of the acoustic detector and simplifying optical path alignment. A non-resonant PAC was employed to amplify the acoustic wave, while a self-designed T-head QTF served as the detector. The acoustic field distribution of the non-resonant PAC was simulated using the finite element method, and experimental verification confirmed that the sound pressure remained nearly uniform. To verify the reliability and stability of the NR-QEPAS sensor, a series of comprehensive experiments was conducted.

With the help of a thermoviscous acoustics module, a non-resonant PAC model was established using the finite element method. The size of the non-resonant PAC was determined to be 4 mm in diameter and 12 mm in length. When the frequency is 8690 Hz, the sound pressure distribution of the selected cutoff line on the surface of the non-resonant PAC is shown in Fig. 1. The sound pressure at the end of the non-resonant PAC was 1.52×10−7Pa and in the middle was 1.64×10−7Pa, with a difference of about 8%, which is approximately equal. When decreasing the diameter and length of the non-resonant PAC, its first-order resonant frequency will increase, and the maximum sound pressure and the minimum sound pressure are closer to each other under the condition of 8690 Hz. On the contrary, when increasing the diameter and length of the non-resonant PAC, its first-order resonant frequency will decrease, and the difference between the maximum sound pressure and the minimum sound pressure under the condition of 8690 Hz will become larger. Considering the dimensions of the self-designed T-head QTF and the simplicity of the optical path alignment, the final diameter was determined to be 4 mm and the length was determined to be 12 mm. In theory, when the modulation frequency of the light source is much smaller than the first-order resonant frequency of the PAC, the sound pressure in the non-resonant PAC is equal everywhere. While in practice, due to the influence of boundary reflections, the sound pressure distribution is approximately equal.

The schematic diagram of the CH4-NR-QEPAS sensor is shown in Fig. 2. Methane (CH4) was chosen as the target gas to validate the sensor’s performance. The CH4 absorption line located at 1650.96 nm was adopted to obtain a strong photoacoustic signal. A near-infrared distributed feedback (DFB) diode laser served as the excitation source. When the emission wavelength matches the selected absorption line, the operating temperature and driving current of the laser should be 35°C and 191.8 mA, respectively. The current of the laser ranged from 176.3 to 207.3 mA in this experiment. The laser beam passed through a collimator and was incident into the non-resonant PAC to excite the photoacoustic signal. Three small holes were opened on the side of the non-resonant PAC, and the positions of the holes were located at 2, 6, and 10 mm from the non-resonant PAC. The photoacoustic signal emission from each hole was detected by the self-designed T-head QTF to verify that the sound pressure signal in the non-resonant PAC is approximately equal. Wavelength modulation and second harmonic (2f) detection technology were implemented in this system. The function generator was utilized to produce a low-frequency ramp wave with a frequency of 10 mHz to scan the laser wavelength across the selected gas absorption line, while the lock-in amplifier generated a high-frequency sine wave for wavelength modulation, thereby exciting the gas to generate a photoacoustic signal. The integration time of the lock-in amplifier was set to 200 ms and the detection bandwidth was set to 405 mHz. Last, the produced piezoelectric signal from the QTF was demodulated by the lock-in amplifier.

Firstly, the resonant frequency f0 of the self-designed T-head QTF was measured using the optical excitation method. The frequency response curve and the physical diagram of the T-head QTF are shown in Fig. 3. After squared normalization and Lorentz fitting of the measured data, the f0 of the QTF was determined to be 8690.55 Hz, and the response bandwidth Δf was 0.92 Hz. According to the relation Q=f0/Δf, the Q factor was calculated as 9446.25. In the later experiments, the modulation frequency was set to be half of f0, which was 4345.275 Hz.

Modulation depth is one of the most vital parameters affecting the detection performance. Therefore, to obtain the strongest photoacoustic response, the modulation depth should be optimized. The relationship between the modulation depth of the sensor and the normalized 2f signal is shown in Fig. 4. It can be observed from the figure that with the increase of modulation depth, the normalized 2f signal shows a trend of rapid increase followed by slow decrease. When the normalized 2f signal was maximum, the optimum modulation depth was determined to be 0.63cm−1.

After determining the resonant frequency of the T-head QTF and the optimum modulation depth, the 2f signal at the three positions of the non-resonant PAC was separately detected to verify whether the actual result is consistent with the simulation. When measuring the sound pressure signal in one hole, the other two holes were closed by pasting copper sheets to prevent leakage of the sound pressure. The QTF was placed sequentially at the left, middle, and right holes of the non-resonant PAC. The prong gap of QTF was directly facing the holes, and the position was adjusted to obtain the maximum photoacoustic signal. The 2f signal of the sensor was measured at a concentration of 20000 ppm (1 ppm = 10⁻⁶) of CH4, and the result is shown in Fig. 5. As can be seen from this figure, when the QTF is located in the left and right holes, the 2f signals basically overlap, in which the peaks of the 2f signals are 36.92 and 37.15 µV, respectively. When QTF is located in the middle hole, the peak of the 2f signal is slightly higher than that of the left and right holes, which is 38.13 µV. The peak in the middle hole is only about 3% higher than that of the left and right holes, which is in accordance with the simulation. It is verified that the sound pressure inside the non-resonant PAC is nearly uniform throughout. In the later experiment, QTF was placed at the position of the middle hole for detection.

The 2f signals of QEPAS, NR-QEPAS, and off-beam QEPAS were measured under the CH4 concentration of 20000 ppm, and the comparison among QEPAS, NR-QEPAS, and off-beam QEPAS is shown in Fig. 6. As can be seen from this figure, the peak value of the 2f signal of QEPAS is 23.53 µV, while the peak value of the 2f signal of the middle hole in NR-QEPAS is 38.13 µV. Compared with QEPAS, the peak value of the 2f signal of NR-QEPAS has increased by a factor of 1.62, which indicates that the non-resonant PAC also has the effect of amplifying the sound wave. Although the peak value of the 2f signal of off-beam QEPAS is 62.40 µV, which is higher than that of NR-QEPAS, the NR-QEPAS sensor has the advantages of not requiring frequency matching and allowing QTF to be placed in any position.

The concentration response of the CH4-NR-QEPAS sensor was verified with different concentrations of CH4. A bottle of pure nitrogen (N2) and a bottle of 2% CH4:N2 gas were used to mix and produce various concentrations of CH4, and the total gas flow rate was set to 360 mL/min. The 2f signal of the NR-QEPAS sensor at different CH4 concentrations is shown in Fig. 7(a). The relationship between CH4 concentration and the peak of the 2f signal is shown in Fig. 7(b). The value of R-square is determined to be 0.999 after linear fitting, implying an excellent linear relationship between CH4 concentration and the peak of the 2f signal. The background noise of the CH4-NR-QEPAS sensor is shown in Fig. 7(c). The standard deviation of the system noise is found to be 46.29 nV and the minimum detection limit (MDL) of this sensor is calculated to be 24 ppm.

To assess the long-term stability of the NR-QEPAS sensor, pure N2 was vented into the gas chamber for more than 2.5 h to calculate the Allan deviation. Figure 8 shows the Allan deviation result of the NR-QEPAS sensor. As can be seen from the figure, with the increase of the average time, the Allan deviation shows a trend of initially decreasing and then increasing. Furthermore, the MDL of this sensor could be improved to 1.09 ppm when the average time was 760 s.

In conclusion, an NR-QEPAS sensor is proposed in this paper for the first time, to the best of our knowledge. It has multiple advantages, including arbitrary QTF positioning, frequency-matching-free operation, and simplified optical alignment. Firstly, using the finite element method, the sound pressure characteristics of the NR-PAC were simulated to validate the feasibility of the proposed scheme. Experimental results confirmed that the sound pressure within the cell remained nearly uniform. The concentration response of the NR-QEPAS sensor was evaluated using different CH4 concentrations. The peaks of 2f signals were linearly fitted and the R-square was determined to be 0.999, implying an excellent linear concentration response of the NR-QEPAS sensor. The MDL of this sensor was found to be 1.09 ppm when the average time was 760 s.