Trace gas sensing technology is used to detect gases at extremely low concentrations^[1-4], widely applied in environmental monitoring, industrial safety, and medical diagnosis^[5-9]. Among the various gas detection methods, electrochemical and semiconductor sensors detect gases through chemical processes and changes in electrical properties^[10]. Both types of sensors generally have the problem of poor stability and are sensitive to environmental disturbances^[11]. In comparison, optical gas sensors operate on laser absorption principles, which avoid the above issues^[12-24]. Meanwhile, it also exhibits multiple advantages including rapid response, high selectivity, and sensitive and non-destructive sensing^[25-29], therefore, becoming a research hotspot in the field of trace gas sensing at present. One of the most representative optical sensing techniques is quartz-enhanced photoacoustic spectroscopy (QEPAS), which was originally proposed in 2002^[30]. In a QEPAS system, a modulated laser beam is directed into the target gas. The gas absorbs the laser energy, leading to periodic thermal expansion that generates acoustic waves via the photoacoustic effect^[31]. A quartz tuning fork (QTF) is used as an acoustic transducer. When the acoustic wave frequency matches the resonance frequency of the QTF, the QTF will resonate^[32]. Based on the piezoelectric effect of the quartz material, an electrical signal will be produced, from which gas concentration can be derived. Benefiting from the QTF’s tiny size, high quality factor, and strong noise immunity^[33,34], QEPAS systems feature the merits of high detection sensitivity and compact structure^[35,36].

In QEPAS systems, based on the principle of acoustic resonance, the signal amplitude can be improved using an acoustic micro-resonator (AmR)^[37]. According to the different configuration methods, the AmR-enhanced QEPAS systems were categorized into two types. One is called on-beam mode^[38,39], initially proposed by Kosterev et al. in 2002. In this mode, two tubes with an inner diameter of 0.32 mm were placed on both sides of the QTF. However, this method has challenges in lasers coupled with dual tubes and suffers from the risk of contact between the laser and QTF, resulting in a large optical noise. To address these limitations, Liu et al. introduced another AmR configuration method called off-beam mode in 2009^[40]. In this configuration, the QTF is placed on the side of AmR, and the sound pressure signal leaks through a slit to the QTF^[41-44]. Compared to on-beam mode, optical alignment becomes simpler, and a shorter length of resonant tube can be used, which can make the detection unit more compact^[45]. However, to date, the off-beam QEPAS sensors employing AmRs utilize only a single QTF to detect photoacoustic signals^[46-48]. If multiple QTFs are used simultaneously, the amplitudes of the signals detected by each QTF could be summed^[49-51], significantly improving the detection performance of QEPAS systems.

In this paper, to overcome the issue of traditional QEPAS systems in terms of low acoustic field energy utilization, a novel single off-beam exciting dual-QTF resonance-enhanced QEPAS system is proposed for the first time, to our knowledge. This innovative system architecture integrates a specially designed off-beam AmR with dual-QTF collaborative detection. This system improves the original off-beam AmR by creating dual holes on both sides of the region with the strongest acoustic field. Two QTFs aligned with the holes detect the photoacoustic signal simultaneously. The signal detected by each QTF is added as the inverse signal of gas concentration. The reported sensor allows for a more complete utilization of acoustic energy, which can improve the sensor’s performance effectively.

Using the finite element analysis method, simulation models were established for the traditional off-beam QEPAS system and the single off-beam exciting dual-QTF system. The AmR was configured with a length of 8 mm, an inner diameter of 0.5 mm^[40], and a wall thickness of 0.15 mm. A linear power source of 15 mW was positioned within the AmR to simulate the laser source. Comparative simulations were performed on both systems under single-hole and dual-hole configurations, with a hole diameter of 0.3 mm. Under the coupling of pressure acoustics, solid mechanics, and electrostatic field, the results of sound pressure distribution and displacement in the system are shown in Figs. 1(a) and 1(b), demonstrating the acoustic field distributions of the two structures under identical conditions. The results indicate that the acoustic pressure reaches its maximum at the center of the AmR. Notably, the acoustic pressure magnitude in the dual-hole configuration is approximately 80% of that in the traditional single-hole system. Based on this result, the dual-QTF design enables a 1.6 times signal enhancement. Figures 1(c) and 1(d) display the displacement characteristics of the QTFs. Although the single-fork displacement amplitude of the dual-QTF system is about 76% of the single-QTF system, the total signal value enables a 1.52 times enhancement. This is roughly the same as in the sound pressure simulations.

The experimental setup is depicted in Fig. 2. Water vapor (H2O) existing in the air was chosen as the target with a concentration of 0.33%; the experiment was conducted under standard ambient temperature and pressure. Given the potential atmospheric fluctuations inherent to the open-air setup, we employed an electrochemical sensor for real-time monitoring and calibration of the water vapor concentration. A continuous wave distributed feedback (CW-DFB) diode laser with a central wavelength of 1.368 µm was employed as the excitation source, targeting the H2O absorption line at 7306.7cm−1. In the experiments, a commercially standard QTF with a resonant frequency (f0) of 32.768 kHz (in vacuum) was used as the photoacoustic detector. Wavelength modulation spectroscopy (WMS) combined with the second harmonic (2f) demodulation technique was implemented in the 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. Meanwhile, a high-frequency sinusoidal signal at f0/2 from the lock-in amplifier was employed to modulate the laser emission wavelength. During the experiments, the injection current of the CW-DFB laser was scanned from 52 to 122 mA to ensure the integrity of the scanned 2f signal. To align with the peak of the gas absorption line, the laser was operated at a central current of 99.6 mA with a temperature of 28°C. Under this driving condition, the laser delivered an output power of 16.3 mW. In the system, the modulated laser was collimated by a fiber collimator (FC) and passed through the designed off-beam AmR. The measured results showed that the laser power was 14.1 mW and the laser transmittance was 86.5%. Two symmetrically positioned holes were fabricated on both sides of the AmR center, and two standard commercial QTFs were used as detectors whose prong space aligned with the two holes. The diameter of the holes was set to 0.3 mm to match the prong spacing of the QTF. The distance between the AmR and the QTF was set to 50–100 µm. In addition, the hole of the excitation position was determined by the optimal laser alignment height according to the traditional QEPAS sensor, located at 0.7 mm from the top of the QTF. The electrical signals from each QTF were added and processed by a lock-in amplifier with an integration time of 200 ms, and the detection bandwidth was set to 405 mHz.

The reported sensor required dual QTFs for signal detection. To ensure synchronization of vibration phases and maximize energy coupling efficiency, precise frequency matching between QTF1 and QTF2 is critical for obtaining the maximum signal amplitude. In the acquisition of resonance frequency, the method of light excitation was applied. The laser injection current was stabilized at 99.6 mA to align the emission wavelength with the H2O absorption peak. Figure 3 displays the normalized squared voltage amplitude of the QTFs as a function of sinusoidal modulation frequency, superimposed with Lorentzian fitting curves. From the fits, the resonance frequencies of QTF1 and QTF2 were determined as f1=32757.36Hz and f2=32756.98Hz, with corresponding bandwidths Δf1=5.36Hz and Δf2=6.54Hz. The minimal frequency mismatch of 0.38 Hz between the QTFs demonstrates acceptable pair-matching characteristics. The quality factors, calculated via the relationship Q=f/Δf, yielded values of Q1=6111.44 and Q2=5008.61. The frequency measurement of the entire dual-QTF system is carried out, and the result is 32757.21 Hz. This frequency is between the frequencies of the two QTFs, and it is taken as the modulation frequency of the dual-QTF system.

Due to the WMS technique used in this system, the 2f signal amplitude exhibits a strong dependence on the laser wavelength modulation current. Consequently, modulation current optimization is required to achieve maximum sensor response. Figure 4 presents the 2f signal amplitude versus laser modulation current derived from off-beam QEPAS measurements using QTF1. Experimental results demonstrate that the 2f signal amplitude initially increases rapidly with modulation current before reaching saturation, peaking at 54.55 mA. This 54.55 mA current value was identified as the optimal modulation parameter and subsequently adopted for all following measurements.

Following the selection of matched QTFs, systematic optimization of the AmR tube length was conducted to maximize the signal amplitude. The parameter of the AmR was optimized by the experiment based on the single-hole AmR first. To maximize the signal amplitude, the inner diameter of the AmR was minimized while ensuring complete laser transmission, resulting in inner and outer diameters of 0.5 and 0.8 mm. In the system, the signal enhancement effect was found to correlate with the AmR length. Experimental results demonstrated that the highest signal enhancement was achieved when the AmR length (L) satisfied λs/2<L<λs, where λs is the acoustic wavelength. With the QTF positioned as close as possible to the hole, measurements were conducted using AmRs with different lengths. AmR lengths ranging from 5 to 11 mm (in 1 mm increments) were systematically tested using single-hole configurations. The 2f signal amplitudes varying with lengths of off-beam AmR are shown in Fig. 5. The results demonstrate that the 2f signal intensity initially increases and then decreases with increasing AmR length. When the length was 7 mm, the signal intensity reached the maximum. Therefore, in the subsequent experiments, a 7 mm dual-hole AmR will be adopted.

To verify both the enhanced performance of dual-hole AmR over the single-hole configuration and the optimal signal superposition when using dual QTFs, five experimental configurations were implemented: bare QTF-based QEPAS, single-hole AmR with QTF1, dual-hole AmR with QTF1, dual-hole AmR with QTF2, and dual-hole AmR with both QTF1 and QTF2. The experimental results are presented in Fig. 6. As can be observed, under identical experimental conditions, the designed off-beam AmR exciting dual-QTF system (dual-hole based QTF1 + QTF2) demonstrated a signal amplitude of 187.63 µV. When employing the same AmR with a single-QTF configuration, the system yielded signals of 98.69 µV using QTF1(dual-hole based QTF1) and 90.46 µV using QTF2 (dual-hole based QTF2). The actual added signal exhibited a 1.52 µV loss compared to the ideal summation, attributable to residual frequency discrepancies between the two QTFs and inherent summation losses in the additive circuitry. The traditional single-hole off-beam AmR configuration with QTF1 and QTF2 produced a signal amplitude of 130.09 µV (single-hole based QTF1) and 116.04 µV (single-hole based QTF2), where the observed signal reduction compared to dual-hole configurations arises from acoustic pressure leakage through the secondary aperture. Additional measurements revealed that the bare QTF has a signal level of 12.49 µV. In comparison, the single-AmR exciting dual-QTF system demonstrated significant signal enhancement factors of 1.44 times and 1.62 times relative to single-hole AmR configurations with QTF1 and QTF2, respectively, yielding a mean enhancement factor of 1.53 times. Remarkably, this configuration achieved a 15.02 times signal amplification compared to the bare QTF system.

By tuning the laser wavelength to a position away from the H2O absorption line, the noise of the above five combinations was measured, and the results are presented in Fig. 7. The noise level of the bare QTF system is higher than the other combinations, primarily because the laser beam must traverse the prong gap of the QTF, introducing substantial optical noise. The noise level of the dual-QTF system is slightly higher than that of the single-QTF system, as the increase in openings and QTFs enhances the noise to a certain extent. In terms of the signal-to-noise ratio (SNR), the SNRs of the dual-QTF system, single-QTF system, and bare QTF are 4726, 3603, and 277, respectively. Comparative analysis shows that the SNR of the dual-QTF system is 1.31 times higher than the single-QTF system, and 17.06 times higher than the bare QTF system. The normalized noise equivalent absorption coefficient (NNEA) of the single-QTF system is 3.67×10−8cm−1·W·Hz−1/2, while that of the dual-QTF system is 2.79×10−8cm−1·W·Hz−1/2, representing a 24% reduction. Based on these results, the minimum detection limit (MDL) of the QEPAS sensor based on dual QTFs is determined to be 698 ppb (parts per billion).

In this paper, a single off-beam AmR exciting dual-QTF-based QEPAS trace gas sensing technique was reported for the first time, to our knowledge. The structural parameters of the proposed sensor are designed based on the standing wave enhancement phenomenon. By creating dual apertures on both sides of the strongest region of the acoustic field, this design improves the efficiency of acoustic field energy utilization while retaining the advantages of the original off-beam configuration. A CW-DFB diode laser with a central wavelength of 1.368 µm was employed as the excitation source. A commercially standard QTF with a resonant frequency of 32.768 kHz was used as the photoacoustic detector. The performance of this QEPAS sensor was evaluated using H2O as the target gas, with optimal performance achieved by fine-tuning the length of the AmR. Compared with the bare QTF system, the experimental results show that the signal is enhanced by 15.02 times and the SNR is 17.06 times higher. Compared with the traditional off-beam QEPAS sensor, the signal is enhanced by 1.53 times and the SNR is 1.31 times higher. Although the sensor demonstrated here is based on QEPAS, its design is highly scalable for extension to dual-resonance photoacoustic spectroscopy (PAS) systems or integration with laser-induced thermoelastic spectroscopy (LITES), enabling deeper signal enhancement. Notably, challenges like cross-technical coupling optimization and system integration complexity may arise during method adaptation.