Three-dimensional optical path extended gourd-type photoacoustic cell for highly sensitive trace acetylene sensing

Abstract

A novel gourd-type photoacoustic cell (GTPAC) has been developed, featuring a highly reflective, polished gold film-coated inner wall that minimizes optical loss and maximizes light utilization efficiency. GTPAC integrates two coupled spherical chambers with a radius ratio 2:3, which is close to the golden ratio. Its unique Gaussian curvature distribution enables multi-directional, disordered light beam reflection without complex optical alignment. It creates a non-periodic three-dimensional (3D) optical trajectory, significantly enhancing light-molecule interactions. GTPAC achieves an exceptionally high sensitivity of up to 3.36 μV/ppm using a distributed feedback butterfly laser with central wavelength of 1532 nm (±1.5 nm) to detect acetylene gas. When the integration time is extended to 100 s, the minimum detection limit is as low as 0.59 ppb. Moreover, its flexible design and broad spectral compatibility enable significant potential for extension to other gases, such as methane and nitrogen oxides, offering new prospects for ultra-sensitive trace gas detection.

1. Introduction

Laser spectroscopy technology, with its real-time online detection, high sensitivity, strong resistance to electromagnetic interference, and rapid response capabilities, has been widely applied in fields such as atmospheric environmental monitoring, medical disease diagnosis through respiratory analysis, industrial chemical safety production, and electrical facility protection [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. Among these, photoacoustic spectroscopy (PAS) sensing technology, based on the photoacoustic (PA) effect [16], [17], [18], [19], [20], has demonstrated significant importance and application value in trace gas detection due to its advantages of zero background measurement interference and relatively simple structure [21], [22], [23], [24], [25], [26], [27].

The PA effect forms the basic principle of PAS sensing technology: when a medium absorbs light energy, a non-radiative relaxation process occurs, causing changes in local spatial density or pressure, which in turn generate acoustic signals. This technology detects and analyzes these acoustic signals to achieve high-precision inversion of medium concentration and characteristics. In this system, the photoacoustic cell (PAC) is a key component for enhancing the PA effect, and its design directly determines the core performance indicators of the PAS sensing system, such as detection sensitivity and signal-to-noise ratio (SNR). In recent years, through iterative optimization of the geometric shape and material properties of the PAC, various structures have been developed, including T-type PAC [28], [29], [30], [31], H-type PAC [32], [33], spherical PAC [34], [35], [36], differential PAC (DPAC) [37], and Helmholtz-type PAC [38]. These PAC structures effectively enhance acoustic resonance signals, optimize the efficiency of light-gas molecule interactions (L-GMI), and suppress environmental noise and background interference. Their design principles also lay the foundation for subsequent PAC structural optimization.

For traditional PACs, the interaction distance between light and matter is generally limited by the length of the cavity itself, resulting in a significant waste of light energy. The introduction of optimization methods can extend the L-GMI path, thereby improving light energy utilization and enhancing the performance of the detection system. To illustrate this, Zhang et al. proposed a PAS acetylene (C₂H₂) sensor based on a reflection cavity-enhanced DPAC, where the reflection cavity consists of two prisms of different sizes, causing the reflected light to travel back and forth four times within the DPAC, resulting in a 3.55-fold improvement in detection performance compared to detection systems without a reflection cavity [39]. Wu et al. ceased the implementation of external reflector devices and instead developed a C₂H₂ sensor based on a balloon-type PAC coated with a highly reflective acetate film on its inner wall. By repeatedly passing light through elliptical foci under periodic conditions, the L-GMI path is effectively extended [40]. Li et al. reported a highly sensitive Helmholtz-type PAC based on multiple reflections, in which excitation light is repeatedly reflected within a single gold-plated cylindrical absorption cavity to extend the absorption path length, ultimately forming periodic optical trajectory characteristics on a two-dimensional (2D) plane [41]. Optical system designs based on mirrors typically face complex challenges in precise alignment. Additionally, periodic conditions often limit methods that extend the optical path by coating the PAC cavity with high-reflectivity thin films. These factors prevent the optical trajectory from effectively covering the interior of the cavity, thereby affecting the maximization of light energy utilization.

In this work, to effectively extend the L-GMI path, a PAS trace C₂H₂ sensing system based on a novel gourd-type photoacoustic cell (GTPAC) has been proposed, with its inner wall coated with a highly reflective (∼99 %) gold film. The gourd-shaped structure provides a natural double-sphere buffer chamber with a 2:3 radius ratio approximating the golden ratio, designed to disrupt periodic reflection conditions. The coupling structure at the top is combined with a converging resonant cavity, resulting in non-uniform Gaussian curvature between the interfaces. Consequently, the necessity for precise and complex optical path design is eliminated; simply designing a 37.4° inclined off-axis incidence at the bottom of the buffer chamber enables the formation of disordered three-dimensional (3D) optical trajectories through multiple reflections, effectively traversing and covering the internal space of the GTPAC. Subsequently, finite element analysis is used to optimize the parameters of the converging resonant cavity, further amplifying the PA signal. By introducing a simple and efficient non-periodic 3D optical trajectory design, the L-GMI path has been significantly extended, with sensitivity improved to 3.36 μV/parts per million (ppm). At an integration time (IT) of 100 s, the minimum detection limit (MDL) for C₂H₂ has been achieved at 0.59 parts per billion (ppb), providing a novel solution for developing ultra-high-sensitivity trace gas sensing.

2. GTPAC geometric design and simulation analysis

2.1. GTPAC design and process

Fig. 1 depicts the distribution of C₂H₂ molecules within GTPAC and the trajectory characteristics of the partial 3D optical path. The purpose is to accurately simulate the process of C₂H₂ molecules migrating into the interior of the GTPAC within a specific piping system and vividly demonstrate the interaction between these molecules and modulated laser beams. This interaction induces a transition of molecules from a steady state to an excited state, which subsequently undergoes a radiationless relaxation process, producing acoustic waves.

Fig. 1.

Schematic diagram of the principle based on GTPAC.

As the core component for photo-thermal-acoustic signal conversion, the GTPAC can effectively amplify PA signals. It is evident that the meticulous design of GTPAC is pivotal in ensuring optimal sensing system performance. Fig. 2(a) illustrates the GTPAC's structural details from a sectional perspective. The core design of GTPAC lies in its coupled cavity structure. It uses two spheres with a radius ratio of 2:3 as the primary and secondary buffer cavities. Although this ratio is a simple integer ratio, it is significant because it approximates the golden ratio (∼1.618). This ingenious choice of an irrational number eliminates the possibility of periodic simplification of optical trajectories from a mathematical standpoint, forcing light to undergo maximum non-periodic diffusion and traversal within the coupled space. This ensures uniform and efficient light energy utilization and simplifies engineering design and manufacturing processes while preserving the aesthetic harmony inherent in the near-golden ratio. Based on this, a converging resonant cavity precisely aligned with the central axis is integrated at the top of the coupled structure, serving as the final energy convergence point. These elements work together to form an efficient light energy "capture" and "constraint" system, aiming to confine light energy within the GTPAC and achieve maximum utilization efficiency. The collimated laser beam is intentionally designed to enter at an angle of approximately 37.4°off-center to prevent the light from shooting out directly. Meanwhile, the gas inlet and outlet are strategically located on one side of the primary buffer chamber, positioned away from the end of the converging resonant cavity. This layout helps reduce noise induced by airflow disturbances, improving detection accuracy.

Fig. 2.

Introduction to the function and structure of GTPAC. (a) Structural details of GTPAC in 3D section. (b) GTPAC physical object.

Material selection is critical for the stability and noise immunity of C₂H₂ sensing systems during operation. The GTPAC, as illustrated in Fig. 2(b), is composed of brass, and the cavity's inner surface is coated with a highly reflective gold film following precision polishing. This material selection aims to maximize reflectivity to increase the number of reflections while minimizing the absorption of optical energy by the cavity walls, thereby effectively suppressing the generation of thermal noise. Due to the limitations of current manufacturing technologies, a method involving separate machining and assembly is adopted to fabricate GTPAC. This GTPAC's primary component is meticulously divided into two halves along the central axis. These halves are individually polished and plated with a gold film, ensuring the metal's precise and consistent application. To ensure the accuracy of the coupling, the connecting end face is precision-cut using computer numerical control machining technology. This ensures that the closing error of the final assembly is strictly controlled within 0.1 mm. As a result, the precise alignment of each component is guaranteed. Finally, mechanical fastening is achieved using bolts, while silicone rubber seals are embedded within the joint between the two halves of the GTPAC to ensure airtightness.

2.2. GTPAC parameter optimization

To achieve effective optical extension within the GTPAC, ray-optical simulations of the GTPAC cavity are first performed using finite element simulation. As illustrated in Fig. 3(a), the simulated optical trajectory distribution within the cavity at 10 ns is attributable to the oblique incidence design at the laser entrance, enabling the laser to be reflected multiple times within the cavity. Specifically, the Gaussian curvature ratio of the double spheres is designed to be an irrational number, which significantly enhances disorder when coupled with a converging resonant cavity, thereby disrupting periodic reflection conditions. The differentiated Gaussian curvature between the combined interfaces results in diversity in the direction of the reflective interface. When light undergoes multiple reflections within the double-sphere structure, even if it comes into contact with the gold-plated inner walls of the converging resonant cavity, its unique converging morphology immediately guides it back into the double-sphere region. This design cleverly prevents light from escaping the system, ensuring maximum light energy utilization. After multiple such disordered superimposed reflections, as shown in Fig. 3(b), the light ultimately forms a 3D non-periodic optical trajectory, efficiently traversing the entire internal space of the GTPAC.

Fig. 3.

Ray optics simulation diagram based on GTPAC. (a) 10 ns trajectory design 2D diagram. (b) 100 ns trajectory distribution 3D diagram.

In the light-heat-acoustic conversion stage, the extension of the L-GMI path increases the effective light power, thereby improving the conversion efficiency of photo-to-thermal energy. In contrast, optimizing a resonant cavity's acoustic characteristics can enhance the heat-to-acoustic energy conversion efficiency. Consequently, the acoustic pressure response amplitude is identified as a pivotal metric for assessing the efficacy of acoustic simulation in this study.

To investigate the acoustic properties of the GTPAC, a finite element analysis based on the theory of thermo-viscous acoustics is conducted using finite element simulation. This analysis accurately models and optimizes the converging resonant cavity to generate acoustic standing wave modes. These modes facilitate acoustic resonance when the PA signal reflects multiple times within the cavity, enhancing the PA signal. As demonstrated in Fig. 4(a), the numerical optimization of GTPAC involves several critical parameters. These include the parameters of the primary and secondary buffer cavities (small sphere radius Ra, large sphere radius Rb, and sphere center distance c) and the parameters of the converging resonant cavity. Notably, the radius a and eccentricity e values at the termination of the resonant cavity are directly related to the acoustic pressure gain level of the GTPAC. Consequently, a parametric scanning method is employed to analyze these parameters systematically.

Fig. 4.

Acoustic characterization simulation of the GTPAC's converging resonant cavity. (a) Parametric details of the GTPAC structure. (b) Parametric scan results for the end radius a of the resonant cavity. (c) Parametric scanning results of eccentricity e.

In order to actualize the miniaturized design of the GTPAC and align it with the characteristics of the 3D optical trajectory, the length b of the converging resonant cavity is initially set to 15 mm. After this, a parametric scan is conducted on a within the range of 0.8 mm to 1.4 mm. As demonstrated in Fig. 4(b), as a increases, the acoustic pressure amplitude at the end of the cavity first increases and then levels off, while the resonance frequency gradually decreases. After careful consideration, a is determined to be 1.3 mm. Additionally, a parametric scan of e is performed in the range of 4–9. As demonstrated in Fig. 4(c), as e increases, the acoustic pressure amplitude decreases. In order to prevent e from being too low and causing the resonant cavity's converging effect to be poor, which in turn causes the light to escape from the GTPAC, e is finally determined to be 5.2. Following a thorough evaluation of the manufacturing process errors, simulation results, and experimental conditions, the specific geometric structure parameters of GTPAC are ultimately determined, as illustrated in Table 1.

Table 1.

Geometrical parameters of customized GTPAC.

e	a(mm)	b(mm)	c(mm)	Ra(mm)	Rb(mm)
5.2	1.3	15	10	10	15

After determining the pivotal parameters of the GTPAC structure, the analysis of the acoustic pressure response modes at the end of the converging resonant cavity will be the focal point of this study. Fig. 5(a)-(d) illustrates the 3D acoustic pressure distributions of distinct resonant modes within the end of the cavity region. The analysis indicates that in the 1st resonance mode, the resonance peak occurs at 3.996 kHz, where the acoustic pressure amplitude is approximately 1.4 times that of the 2nd, 15.5 times that of the 3rd, and 1.7 times that of the 4th resonance mode, respectively. Furthermore, through an analysis of the coupling mechanism between the double-sphere buffer chamber and the resonant cavity, it is found that when their resonant frequencies are close, modal coupling and energy exchange cause the resonant cavity's natural frequency to shift, resulting in pseudo-harmonic characteristics and ultimately leading to abnormal spectral compression between the 2nd and 3rd resonant modes [42]. Therefore, selecting an appropriate modulation frequency far from this resonance mode interference is important.

Fig. 5.

GTPAC acoustic pressure mode finite element simulation analysis. (a)-(d) 3D acoustic pressure mode cloud maps from the 1st resonance mode to the 4th resonance mode. (e) Frequency response curves of the first four acoustic resonance modes at the end of resonant cavity.

After configuring the sweep frequency analysis to a step size of 10 Hz in the finite element simulation, the frequency response curve depicted in Fig. 5(e) is obtained. The curve demonstrates that the peak acoustic pressure of the 1st acoustic mode is significantly higher than that of the 2nd, 3rd, and 4th resonance modes. Furthermore, the sensing system's operating frequency is set to 3.996 kHz, corresponding to the 1st resonance mode. This frequency selection strategy has two significant advantages. First, it effectively circumvents the interference of 1/f low-frequency noise in the experimental environment [43]. Second, it uses the high acoustic pressure frequency response characteristics of this resonance mode, which significantly enhance the sensitivity of the sensing system and optimize the SNR.

2.3. Summary of GTPAC

The final optimized simulation results are shown in Fig. 6. In summary, the GTPAC is formed by combining a double-sphere buffer chamber with a converging resonant cavity (with volumes of approximately 1.52 cm³ and 0.22 cm³, respectively). Through ray optical simulation, the incident angle is determined to be 37.4° to form a non-periodic optical path. Through simulation optimization, the radius a of the tail end of the converging resonant cavity is set to 1.3 mm, the eccentricity e is set to 5.2, and the 1st resonance frequency of 3.996 kHz is selected as the excitation light modulation frequency. By measuring the sound pressure at the end face of the resonant cavity, the amplitude can reach up to 4.43 mPa. Therefore, the GTPAC formed after optimization of various parameters laid the foundation for the excellent performance of subsequent experiments.

Fig. 6.

The 3D simulation cloud map.

3. Experimental setup

In this work, C₂H₂ is used as the target trace analyte to evaluate the detection performance of a GTPAC-based PAS sensing system. Meticulous consideration is given to selecting the laser light source before constructing the experimental system. Owing to the direct proportionality between the PA signal amplitude and the absorption coefficient of gas molecules for specific optical wavelengths, it is essential to employ a laser source with an operating wavelength band situated at the characteristic absorption peak (fingerprint region) of the C₂H₂ molecule to maximize the PA signal enhancement. The HITRAN database [44] is queried to obtain the near-infrared absorption spectral data of C₂H₂. Even though laser light sources in the mid-infrared band generally possess high absorption coefficients for C₂H₂, the substantial expense of these lasers presently hinders their extensive application. Therefore, this study selected a laser light source operating in the C₂H₂ near-infrared strong absorption peak region. After considering relevant factors, an excitation wavelength of 1532.83 nm is selected to precisely match the strong absorption peak of C₂H₂, thereby enhancing the initial PA signal. Furthermore, this wavelength is located away from the absorption peaks of water vapor, effectively preventing cross-interference from water. This is crucial for maintaining the precision of experimental detection. Prior to initiating the experiment formally, two indispensable preparatory tasks are required. Initially, the entire system's gas channel must be purged with pure nitrogen (N₂) for one minute to ensure complete dryness. Secondly, employing a red laser pointer for observation constitutes a critical step in assessing the feasibility of the optical path design, primarily confirming that light does not escape from the GTPAC. Both of these serve as the fundamental guarantee for obtaining optimal experimental data.

The schematic diagram of the GTPAC-based PAS sensing system is depicted in Fig. 7. The system uses a tunable distributed feedback (DFB) laser with a center wavelength of 1532 nm (±1.5 nm) and exceptional monochromaticity and narrow linewidth, among other characteristics, as the excitation light source. In the application of noise-reduced wavelength modulation techniques, the arbitrary waveform generator (Siglent: SDG2122X) fulfills two critical functions. First, a low-frequency sawtooth wave for scanning the absorption peaks of the C₂H₂ molecule and a high-frequency sinusoidal wave for wavelength modulation are generated. These signals are then superimposed to modulate the laser source. The modulated output beam is transmitted through an isolator to an erbium doped fiber amplifier (Accelink: EDFA-BA-22) for power amplification, increasing the output power to 300.1 mW. Subsequently, the laser is introduced directly into the GTPAC laser inlet through the fiber collimator (Gaussian beam with a beam diameter of less than 0.5 mm and an alignment tolerance of less than 0.1°). Secondly, the same high-frequency sinusoidal waveform is fed into the lock-in amplifier (National Instrument Quantum: OE-1022), serving as a reference signal for the subsequent demodulation of second harmonic (2 f) signals (carrying the information of the C₂H₂ molecule). When the laser scans the absorption peaks of C₂H₂ molecules with a period of 50 s (sawtooth wave frequency of 20 mHz), a portion of C₂H₂ molecules within the GTPAC absorbs the modulated light. These molecules then undergo a non-radiative relaxation process, converting optical energy into heat. This results in a periodic change of local spatial temperature and pressure and, consequently, the generation of a pressure wave (the initial PA signal).

Fig. 7.

Device diagram of the GTPAC-based experimental system. AWG: Arbitrary Waveform Generator, DFB: Distributed Feedback Laser, EDFA: Erbium Doped Fiber Amplifier, E-MIC: Electrical Microphone, PC: Personal Computer.

Guided by simulation results, the sine wave frequency is intentionally tuned at one-half the 1st resonant frequency of the GTPAC to achieve resonant amplification of the 2 f signal to be measured. Subsequently, the PA signal captured by the electrical microphone (BSWA TECH, MPA201) is converted to a weak electrical signal and amplified by a pre-amplifier. The signal is then fed into a lock-in amplifier, configured with a locking time constant of 0.3 s and an attenuation slope of 18 dB/octave, for 2 f signal demodulation and extraction. Subsequently, the extracted 2 f signal data is transmitted to a personal computer (DELL precision 3490) for analysis and processing.

4. Results and discussion

4.1. Analysis of experimental results

Before conducting gas measurement experiments, to ensure the accuracy and reliability of measurement data, it is necessary to wait for the value to stabilize for three minutes after replacing the gas sample before recording the data. As demonstrated in Fig. 8, the frequency response characteristic curve of GTPAC in the 2–2.2 kHz frequency range is accurately described by a Lorentz function, exhibiting high conformity. The fitting process successfully identified the target modulation frequency at 2.115 kHz. Notably, the quality factor achieves a remarkable value of 35.25, validating the GTPAC's high detection sensitivity and robust anti-interference capabilities. Therefore, when the GTPAC operates at a modulation frequency of 2.115 kHz, the theoretically generated 2 f signal frequency should be 4.23 kHz. This finding closely aligns with the observed frequency of the 1st resonant mode in the simulation. The minor discrepancy between the two is hypothesized to be primarily attributable to the deviation introduced by the manufacturing process. To demonstrate better experimental detection performance, 2.115 kHz will be used as the modulation frequency in the subsequent studies.

Fig. 8.

Actual frequency response characteristic curve of GTPAC in the 1st resonant mode.

The ability to detect gases at low concentrations with high precision is a critical metric for evaluating the performance of highly sensitive gas sensors. As illustrated in Fig. 9(a) (inset), the GTPAC-based PAS sensing system exhibits distinct 2 f signal response waveforms for varying C₂H₂: N₂ gas mixture ratios. In order to verify the fitting degree of linear response, the low concentration interval (0.101–100 ppm) of C₂H₂ is selected for 2 f signal peak fitting, and the results are shown in Fig. 9(a). The system demonstrates excellent linear response characteristics and outstanding detection sensitivity over the low concentration range, with a linear fit coefficient of determination (R²) reaching 0.99993 and an exceptionally high sensitivity of 3.36 µV/ppm.

Fig. 9.

Experimental results. (a) Linear response fitting results of the PAS sensing system based on GTPAC for the 2 f peak in the mixture concentration range of 0.101–100 ppm. Inset: 2 f signal response waveforms at different C₂H₂ concentrations. (b) 2 f signal response waveform for C₂H₂ concentration of 0.101 ppm. (c) 300 s accuracy test results at a C₂H₂ concentration of 49.4 ppm. (d) The results of Allen deviation calculations for noise in PAS sensing systems based on GTPAC. Inset: noise level under pure N₂ background conditions.

The SNR is a critical indicator that directly influences the detection accuracy of the PAS sensing system. The SNR is the ratio between the 2 f signal amplitude and the standard noise deviation (1σ) at a specified concentration. Fig. 9(b) depicts the 2 f signal response curve at a C₂H₂ concentration of 0.101 ppm, where the peak-to-peak signal amplitude reaches 2.23 μV, corresponding to an SNR of 56.6. This result indicates that the sensing system maintains excellent detection performance even at sub-ppm C₂H₂ concentration levels. To ensure that the sensor does not produce accidental errors when measuring in a mixed gas environment, a 300 s continuous operation test is conducted at a concentration of 49.4 ppm of C₂H₂. The results are depicted in Fig. 9(c). The output 2 f signal exhibited no fluctuations during this period, demonstrating the system's exceptional detection accuracy.

The current findings are preliminary to comprehensively evaluating a highly cost-effective sensing apparatus. To further substantiate the reliability of the GTPAC-based PAS C₂H₂ sensing system, three essential performance evaluation criteria are assessed in this study.

Firstly, the system's sensitivity is quantified using the MDL. The MDL is calculated based on a C₂H₂ concentration of 0.101 ppm and determined to be 1.78 ppb at 0.3 s IT. This result directly reflects the system's excellent performance in detecting trace concentrations of C₂H₂. Secondly, the noise measurement results are evaluated for three hours in a pure N₂ environment using the standard Allan deviation analysis method to demonstrate the system's long-term stability, as shown in Fig. 9(d) (inset). Calculations showed that extending IT to 100 s optimized MDL to 0.59 ppb, as shown in Fig. 9(d). Finally, the NNEA is employed to evaluate the system's noise suppression capability. Under standard laboratory conditions (23°C, 1 atm), the NNEA value is calculated as 9.2 × 10⁻¹⁰ W·cm⁻¹·Hz^−1/2.

4.2. Performance comparison and discussion

To illustrate the effect of the optical trajectory of the design on the experimental results, comparative experiments are conducted at different incidence points under the 1st resonance frequency and the same excitation power. Fig. 10(a) shows that when the optical trajectory appears on the side near the end face of the resonant cavity, its sensitivity reaches as high as 3.36 µV/ppm. However, as shown in Fig. 10(b), when the optical trajectory is only inside the double-sphere buffer chamber, its sensitivity drops to 1.28 µV/ppm, which is less than half of the result at incident point 1. This demonstrates the advantages of the optical trajectory of the GTPAC at the initial incident point 1, highlighting the superior performance of the designed sensing system. However, trajectory optimization is not limited to this, as gaps caused by manufacturing process coupling may lead to light deviation and reduce experimental effectiveness. Furthermore, in practical applications, the modulation frequency of 2.115 kHz may be challenging in meeting noise restrictions in specific scenarios outside of laboratories. Specifically, the GTPAC-based PAS sensing system developed in this study has been shown to possess excellent sensitivity and long-term operational stability in detecting trace concentrations of C₂H₂. Therefore, it is meaningful to optimize its size, optical trajectory, and manufacturing process further to overcome these limitations.

Fig. 10.

Comparison of experiments with different incidence points. Inset: Optical trajectory at 20 ns. (a) Experimental results based on the incident point 1. (b) Experimental results based on the gas outlet as the incident point 2.

To further illuminate the technical advantages of GTPAC, a comparative analysis is conducted between its performance and that of PAS sensing systems based on different PACs. The results of this analysis are presented in Table 2. The data analysis shows that the uniquely designed gourd-shaped reflective cavity enhances the core performance of the sensing system. This cavity extends the L-GMI path, significantly increasing the effective optical power and enhancing the PA signal at the excitation source. Consequently, this enhances performance indicators such as MDL and NNEA.

Table 2.

Comparison of key performance indicators with some C₂H₂ sensing systems.

Resonate	λ (nm)	Transducers	MDL@IT (ppb/s)	NNEA (W·cm−1·Hz−1/2)	Ref.
Yes	1530.3	E-MIC	15.81@100	Not stated	[39]
No	1532.8	Film	50@100	Not stated	[45]
Yes	1532.8	Cantilever	1.1@324	2.2 × 10−8	[46]
Yes	1530.3	E-MIC	5@200	6.48 × 10−9	[47]
Yes	1532.8	Cantilever	40.7@100	4.65 × 10−9	[48]
Yes	1532.8	Cantilever	15@100	2.7 × 10−9	[49]
Yes	1532.8	E-MIC	0.59@100	9.24 × 10−10	GTPAC

5. Conclusions

This study outlines a highly sensitive, high-optical-energy-utilization PAS C₂H₂ sensing system based on a novel GTPAC. The GTPAC uses two coupled spheres with a radius ratio approximating the golden ratio as primary and secondary buffer cavities, combined with a converging resonant cavity. The inner walls of the entire component are coated with high-reflectivity (∼99 %) gold film. Employing the off-axis oblique incidence method effectively suppresses light leakage. Consequently, following multiple reflections, a disordered and complex non-periodic 3D optical trajectory is formed, effectively traversing and covering the internal space of GTPAC. Subsequently, using finite element simulation, finite element simulations based on thermo-viscous acoustics are performed to optimize the key parameters of the converging resonant cavity. According to the simulation results, a is set to 1.3 mm, e is set to 5.2. After comprehensively optimizing both the optical path and the acoustic characteristics, the experiment finding demonstrates an exceptionally high detection sensitivity of 3.36 μV/ppm, and the MDL is 1.78 ppb at 0.3 s IT. When the IT is extended to 100 s, the MDL achieves a lower value of 0.59 ppb, corresponding to an NNEA of 9.24 × 10⁻¹⁰ W·cm⁻¹·Hz^−1/2. Consequently, based on high-quality GTPAC, the PAS sensing system introduces a simple and efficient optical trajectory design to address technical challenges such as the insufficient extension of traditional 2D planar reflective optical paths, uneven spatial reflection coverage under 3D periodic constraints, and the high difficulty in designing high-precision extended optical path systems, exhibits great application potential in trace gas sensing.

CRediT authorship contribution statement

Chunyong Yang: Funding acquisition. Zhongke Zhao: Data curation. Likang Zhang: Methodology. Sixiang Ran: Software. Chuanwen Qian: Writing – original draft, Investigation, Conceptualization. Wenjun Ni: Writing – review & editing. Ping Lu: Resources. Perry Ping Shum: Visualization. Chenyu Wang: Validation.

Funding

This work is supported by the National Natural Science Foundation of China (62171487, 62105373); Natural Science Foundation of Hubei Province (2024AFA030, 2023AFC012); Innovation and Entrepreneurship Training Program Funded by South-Central Minzu University (202510524003).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Biographies

Chuanwen Qian is conducting the research on photoacoustic/photothermal spectrum and its sensing applications. His supervisor is Prof. Wenjun Ni.

Wenjun Ni is an associate professor at South-Central Minzu University, Wuhan, China. He obtained support from the “Wuhan talent” program in 2021, “Hubei high-level talent” program in 2022 and China association for science and technology young talents promotion project in 2025. He was a postdoc (research fellow) at the Centre of Optical Fiber Technology, Nanyang Technological University, from 2019 to 2020 (Supervised by Prof. Perry Shum). Earlier, he got his Ph.D. in Optical Engineering from Huazhong University of Science and Technology, Wuhan, China, in 2019. He focuses on special optical fiber devices, fiber acoustic sensing, and photoacoustic/photothermal spectrum, and has published more than 70 articles.

Chunyong Yang is a professor at South-Central Minzu University. His research interests focus on optical wireless communication. In 2005, he got his Ph.D. from Huazhong University of Science and Technology, China. Currently, he has been the dean of the College of Electronics and Information Engineering at South-central Minzu University since 2018. He has served as the deputy director of the academic committee in the College of Electronics and Information Engineering since 2019.

Zhongke Zhao is conducting the research on photoacoustic/photothermal spectrum and its sensing applications. His supervisors are Prof. Wenjun Ni and Prof. Perry Ping Shum.

Likang Zhang is conducting the research on photothermal spectrum and its sensing applications. His supervisor is Prof. Wenjun Ni.

Sixiang Ran is conducting the research on specialty fiber and its sensing applications. His supervisors are Prof. Chunyong Yang and Prof. Perry Ping Shum.

Chenyu Wang is conducting the research on photoacoustic spectrum and its sensing applications. His supervisor is Prof. Wenjun Ni.

Ping Lu is a professor at the School of Optical and Electronic Information at Huazhong University of Science and Technology, China, and the Next Generation Internet Access National Engineering Laboratory. She got her Ph.D. in optical engineering in 2005 from Huazhong University of Science and Technology. Since 2006, she has worked at the School of Optical and Electronic Information at Huazhong University of Science and Technology, and since 2011, she has been a full professor. Her research mainly focused on fiber sensors, multicomponent trace gas detection, high-sensitivity optical fiber acoustic detection technology, and high-resolution fiber sensor demodulation technology.

Perry Ping Shum is a chair professor and deputy director of scientific research in the Department of Electronics and Electrical Engineering, Southern University of Science and Technology. Director of Guangdong Key Laboratory of Integrated Optoelectronics Intellisense, National Distinguished Expert, IEEE Fellow, Chinese Optical Society Fellow, SPIE Fellow, OPTICA Fellow, President-elect of IEEE Photonics Society. He has published nearly a thousand academic papers with more than 19,000 citations, and a H-index of 66. In recent years, as the person in charge, he has been granted research funds of more than RMB 50 million. He served as Director of the NTRC, OPTIMUS, and COFT, and Dean in charge of education at Nanyang Technological University, Singapore. During this period, NTU-COFT, a world-class fiber research/processing center, was created, which enabled Singapore to manufacture special fiber optics, special fiber lasers, and sensors for the first time. He chaired several major international conferences, including CLEO-PR | OECC| PGC 2017, and initiated international conferences such as ICICS, PGC, ICOCN, ICAIT, OGC, etc.

Data availability

No data was used for the research described in the article.