Gas sensing technology is playing an important role in human production and activities^1-11, and the gas sensor based on laser absorption spectroscopy (LAS) is one of the mainstream types. It offers some unique advantages such as high selectivity, high sensitivity and rapid responsiveness^12-21. According to the different detective modes, the LAS can be segmented into three types: 1) the direct detection technology including tunable diode laser absorption spectroscopy (TDLAS)²²; 2) the cavity enhanced absorption spectroscopy (CEAS)^23-25; 3) and the indirect detection technology whose typical representations are photoacoustic spectroscopy (PAS) and quartz enhanced photoacoustic spectroscopy (QEPAS)^26-29. Among these technologies, PAS inverts the gas concentration by detecting the acoustic signal generated after the laser is absorbed by the gas, and thus it can achieve the no background detection^{30, 31}. QEPAS replaces the traditional microphone with quartz tuning fork (QTF) as a detection element, which can effectively filter the 1/f noise of the system³².

Although QEPAS offers an outstanding performance for gas sensing, there are some shortcomings prevent it from being used in some special application scenarios. For example, since QTF generates an effective signal only when placed in an environment filled with the test gas, QEPAS is powerless to detect the corrosive and acid gases such as hydrogen fluoride (HF), hydrogen sulfide (H₂S) and hydrogen chloride (HCl)^33-35. In order to improve the disadvantages of QEPAS, Ma et al. reported a different detection technology named light-induced thermoelectric spectroscopy (LITES) in 2018³⁶. The detection segment of this method is still QTF, but the signal generation no longer relies on acoustic wave. When the modulated laser is absorbed by the test gas in a gas chamber, the transmitted laser will carry the concentration information of the gas. After absorbing the energy of this part of the laser, the QTF will perform a signal conversion process from light to heat and then to electricity. By demodulating the electrical signal, the concentration information of the gas can be obtained^37-39. In LITES based gas sensors, the QTF needn't be surrounded with the test gas, which makes it possible to achieve non-invasive detection^40-42. In addition, since LITES relies on the thermoelastic deformation generated by the absorption of laser energy to generate current signals, it has an extremely wide response bandwidth compared to traditional photodetectors and is expected to become a means of detecting gases in the full-band spectrum^{43, 44}.

Based on the principle of Beer-Lambert's law, the strength of the absorbed signal in a gas sensing system is proportional to the gas absorption length⁴⁵. Multi-pass cells (MPCs) are usually adopted to increase the absorption length and therefore regarded as a key device to improve the detection performance of LITES system^{46, 47}. Herriott cell is the most widely used MPC because of its simple structure and high stability. In 2019, He et al. firstly reported a LITES sensing system combined with a Herriott cell with an effective absorption length of 10.1 m⁴⁸. Recently, MPCs with dense spot patterns are gradually being used as a new gas absorption device^49-53. MPCs with dense spot patterns have a large ratio of optical path length to volume (RLV) which makes it potentially a key element for integrated ultra-highly sensitive LITES based sensors.

Another vital component in LITES system is QTF^54-56. Currently, the standard commercial QTFs with a resonant frequency of ~32.76 kHz are most commonly used. In order to match the resonance frequency, the system also need a high modulation frequency. In a very short modulation period, the QTF can only absorb a very limited amount of laser energy, and thus converts a weak piezoelectric signal. Using a low-frequency QTF as a detector provides a longer energy accumulation time, which will effectively improve the detection performance of the LITES system.

In this manuscript, a highly sensitive LITES sensor based on a MPC with dense spot pattern and a novel QTF with low frequency is reported for the first time. The MPC has an optical path length (OPL) of 37.7 m, a volume of 272 mL, and forms a spot distribution pattern with 4 concentric rings on the mirrors to enhance laser absorption. Besides, a self-designed trapezoidal-tip QTF with low-frequency of 9461.83 Hz was used to further enhance the sensing performance. Acetylene (C₂H₂) was selected as the target gas for testing to evaluate the sensor performance.

The White cell and the Herriott cell are the two most typical MPCs and have a long history of application in gas sensing^57-59. Especially the Herriott cell has many advantages such as simple structure, stable optical path, and easy adjustment, which makes it almost has been the unquestionable choice in gas sensors. However, it also has some drawbacks that limit further improvements in sensor performance. The spots distribution of it is usually individually circular or elliptical, which makes its mirror utilization extremely low. Furthermore, when the number of reflections increases, spots with adjacent positions tend to overlap and it will introduce interference noise into the system. MPC with dense spot patterns is an improve design of the Herriott cell, which not only retains the previous features, but significantly improves the mirror utilization^{60, 61}.

In order to obtain the parameters of MPC, a computational model based on vector reflection theory was designed. It is capable of tracing beam transmitted by reflection between two identical spherical mirrors placed co-axially. The key parameters in the MPC, including incident position, incident angle, diameter of the mirror, radius of curvature and distance between the two mirrors, are varied to obtain different spot distribution effects. There are several requirements that can be used as criteria for parameter selection: 1) In multiple reflections, the beam does not overflow from the edge of the mirrors unless it is emitted from the set perforation position; 2) Having a regular and non-overlapping spot distribution pattern to facilitate optical path length adjustment and avoid interference noise; 3) Achieving as many reflections as possible with a short base length; 4) The outgoing beam exits the outlet completely with good beam quality.

For convenience, the design of MPC was based on regular-sized mirrors with a diameter of 2 inches (1 inch = 2.54 cm)and a radius of curvature of 100 mm. In order to simulate the spots shape on the mirror, several parallel straight lines were used to construct the beam model, and the diameter of the beam was set to 600 μm. The parameter settings of MPC are shown in Fig. 1(a). The perforation diameter on the mirrors was set to 2 mm to allow for incident and outgoing beams. Based on the established computational model, when the distance of the mirrors, the incident angles θ and Φ were set to 137.78 mm, −7.23° and −5.43°, respectively, and the incident position coordinate was set to 20.18 mm and 3.42 mm, the spot distribution with four concentric circles was obtained. The simulation on the incident mirror is shown in Fig. 1(b). The beam was reflected 274 times and then exits through the exit perforation located on the other side. The volume of the MPCs was considered to be the cylindrical-like region between the two spherical mirrors, which is approximately equal to the volume of sample gas that the gas chamber can hold. The volume of this MPC is 272.6 mL and the OPL is 37.7 m, which gives a RLV of 13.8 cm⁻². Compared to a commercial Herriott cell (HC10L-M02, Thorlabs) whose RLV is about 1.49 cm⁻², there was a ~8-fold improvement. The plano-concave spherical mirrors with through-holes were processed based on the acquired parameters and subsequently coated with silver to achieve a high reflectivity across a broad range of wavelengths. It can provide greater than 95% reflectivity in the wavelength range of 400–12000 nm. The spot distribution obtained using a He-Ne laser is shown in Fig. 1(c). Although the quality of the beam is degraded due to multiple reflections and some of the spots become unclear, the shape of the actual spot still matched well with the simulation.

The QTFs used in this manuscript are shown in Fig. 2(a), and QTF1 and QTF2 represents the commercial QTF and the self-designed trapezoidal-tip QTF, respectively. Compared to the standard commercial QTF, the self-designed QTF has an optimized dimension. A 3D model of the QTF was built based on COMSOL software, and finite element analysis was used to optimize the parameters such as the width and length of the fork fingers as well as the thickness in order to obtain a lower resonance frequency, the highest average charge density and maximum surface stress. In addition, it has a unique trapezoidal tip that enables it to generate a larger piezoelectric signal at resonance, which is because the trapezoidal-tip improves the stress distribution in the fork fingers and facilitates an increase in the Coriolis force and charge generation rate. The resonant frequencies of two QTFs were measured, and the normalized data was fitted using the Lorentz function, as shown in Fig. 2(b). The resonance frequencies (f) of the commercial QTF and the trapezoidal-tip QTF are 32.753 kHz and 9641.83 Hz, with response bandwidths of Δf₁ = 3.12 Hz and Δf₂ = 1.47 Hz, respectively. And the related quality factors (calculated with the formula Q=f/Δf) are 10565 and 6559, respectively. Compared to commercial QTF, the trapezoidal-tip QTF has a ~70% decrease in frequency and is beneficial to increase the energy accumulation time⁶². In addition, instead of using silver-plated electrodes as in commercial QTFs, the trapezoidal-tip QTF uses gold-plated electrodes to reduce resistance.

The schematic of the C₂H₂-LITES sensor based on a multi-pass cell with dense spot pattern is shown in Fig. 3. A strong absorption line of C₂H₂ located at 1530.37 nm (6534.37 cm^–1) was selected to verify the detection performance. The system was equipped with a continuous wave (CW), distributed feedback (DFB) diode laser as the laser excitation source, and the output power was amplified by an erbium-doped fiber amplifier (EDFA). The operating temperature and center current of the laser were set to 29°C and 92 mA, respectively, and the output power of the EDFA was in the range of 300 mW to 1000 mW. The incident beam was initially collimated and subsequently directed through an aperture to reduce the size, and then entered the MPC at a particular angle. After hundreds of reflections, the beam would exit from the other side, two wedge-shaped mirrors were used as the optical windows so that no optical interference occurs. The beam subsequently hit the QTFs by means of a focusing lens. The focal length of the lens is 10 mm and the maximum signal was generated when laser hits the root of a QTF, and the target points on QTFs are shown in Fig. 3.

In order to reduce the background noise, wavelength modulation spectroscopy and the 2nd harmonic demodulation techniques were adopted. A function generator was used to generate a ramp wave with a period of 100 s so that the laser output wavelength was scanned through the target absorption line. The lock-in amplifier generated a sine wave that modulated the laser wavelength and was also used as a reference signal for demodulation. The frequencies of the sine wave were set to half the resonance frequencies of the QTFs. Diode lasers have different wavelength response at different modulation frequencies, which result in different optimal modulation currents. The higher the modulation frequency, the smaller the wavelength response, which means there is a smaller change in wavelength with a unit change of current. Therefore, in order to obtain the same range of wavelength change, a larger modulation current is required at high modulation frequency⁶³. Therefore, the systems using QTF1 and QTF2 had different current modulation depths of 27.36 mA and 19.18 mA, respectively. The integration times of the lock-in amplifier were respectively set to 120 ms and 240 ms for those two QTFs, and the detection bandwidths were 577 mHz and 288.5 mHz, respectively.

Firstly, 2f-LITES signal was measured in 100 ppm C₂H₂:N₂ gas mixture. Figure 4(a) and 4(b) show the variation of the peak values with different output power of EDFA when QTF1 and QTF2 were used as the detectors, respectively, and the insets show the respective 2f signal waveform. The peak value of the 2f-LITES signal has an excellent linear relationship with the optical output power of EDFA. The noise and signal noise ratio (SNR) at different laser powers are shown in Fig. 4(c), when QTF1 and QTF2 were adopted, respectively. The system using two different QTFs has a similar trend. There is a small increase in noise and a significant increase in SNR as the laser power increased. Therefore, all subsequent experiments were performed with the output power of EDFA at 1000 mW, which produced the highest SNR.

Two gas mass flow meters were used to control the flow rate of a bottle of 100 ppm C₂H₂:N₂ standard gas mixture and a bottle of pure N₂ to obtain different concentrations of C₂H₂. It should be noted that the total flow rate of the gas was kept at 240 mL/min. The 2f-LITES signals detected at different concentrations when QTF1 and QTF2 were used as detectors are shown in Fig. 5(a) and 5(b), respectively. At a concentration of 100 ppm, the 2f signal peak measured with QTF1 was 176.92 μV, while the value measured with QTF2 was 250.30 μV. The latter is 1.4 times higher than the former, which can be attributed to the lower resonance frequency of the trapezoidal-tip QTF. This character has led to an extended duration for energy accumulation. Figure 5(c) and 5(d) display the peak values of the 2f signal at various concentrations, as well as the results after linear fitting. Both exhibit an excellent level of linearity.

The background noise was measured when pure N₂ was used to fill the MPC with a flow rate of 240 mL/min and the output wavelength of the laser was locked at the target absorption line of C₂H₂. The standard deviation (1σ) noise obtained from continuous monitoring of 2f amplitude for 60 s and values of 85.50 nV for the system using QTF1 as well as 61.80 nV for the system using QTF2 is shown in Fig. 6. Consequently, the minimum detection limit (MDL) of C₂H₂-LITES sensor using two different QTFs can be calculated from the ratio of the standard gas concentration to the SNR of the corresponding system. The achieved MDL for the C₂H₂-LITES sensor based on QTF1 and QTF2 were 48.3 ppb and 24.6 ppb, respectively. There is an enhancement of the system's detection performance by a factor of 1.96 when replacing the commercial QTF with the self-designed trapezoidal-tip QTF.

The long-term stability of the system can be reflected by the Allan deviations shown in Fig. 7, where Fig. 7(a) shows the results probed with QTF1 and Fig. 7(b) with QTF2. The raw data were obtained by locking the laser output wavelength at the target absorption line and continuously monitoring the 2f signal amplitude for more than 2 hours in a pure N₂ atmosphere. The MDL of the QTF1 based C₂H₂-LITES sensor can be improved to 2.61 ppb when the average time is 100 s and the MDL of the QTF2 based system can be enhanced to 1.29 ppb when the average time is 140 s. Due to its large size of QTF, the system using trapezoidal-tipped QTF had better long-term stability.

In conclusion, a highly sensitive LITES sensor based on a MPC with dense spot pattern and a novel QTF with low resonance frequency is reported for the first time. C₂H₂ was selected as the target gas to examine the performance of the system. The MPC has an OPL of 37.7 m and an excellent RLV of 13.8 cm⁻². Additionally, a self-designed QTF with trapezoidal-tip and low resonance frequency of 9641.83 Hz was used to improve the detection performance. An EDFA was employed to amplify the output power of the used diode laser to further enhance the signal level. At an optical power of 1000 mW, the MDL of the C₂H₂-LITES sensor based on trapezoidal-tip QTF was determined to be 24.6 ppb, which was 1.96 times better than the system using a commercial QTF with a resonance frequency of 32.753 kHz. Allan deviation analysis showed that the MDL of the commercial QTF based C₂H₂-LITES sensor could be reduced to 2.61 ppb at an average time of 100 s, whereas the system using the trapezoidal-tip QTF could achieve a MDL of 1.29 ppb at an average time of 140 s. The detection performance of this system can be further enhanced by designing MPCs with a larger RLV and better output beam quality. In addition, research on the design of new QTFs with low resonance frequency and high Q-factor can further promote the development of LITES technology. Furthermore, the study of QTF structures that enable multiple excitations will also be effective in enhancing the system performance.