## Abstract

We present a novel T-type half-open resonant photoacoustic (PA) cell for trace gas detection. The T-type PA cell has just one buffer volume, and a fiber-optic acoustic sensor is placed at one end of the resonator. Compared with the conventional H-type PA cell, the first-order resonant frequency of the T-type PA cell is reduced by half and the PA signal is enhanced with the same resonator. The T-type resonant PA cell was used in acetylene (C_{2}H_{2}) gas detection system based on PA spectroscopy. Experimental results show that the minimum detectable limit of C_{2}H_{2} is calculated to be 0.70 parts per billion (ppb), which is lower than the traditional H-type PA cell.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Trace gas detection plays an important role in many areas, such as plant and insect respiration studies, atmospheric monitoring, and combustion studies [1–5]. Photoacoustic (PA) spectroscopy (PAS), which is characterized by fast response, overall high selectivity and sensitivity, and compactness of the detection module, is the most versatile method for trace gas analysis [6–9]. The principle of PAS is to detect the sound waves generated from the gas molecules upon absorption of the excitation radiation, whose frequency is resonant with the vibrational or rotational energy levels of the target gas molecule [10–12]. The amplitudes of the PA signals generated in PA cell are proportional to the incident light intensity, sensitivity of acoustic detectors and the PA cell constant [13]. In recent years, many researchers have made efforts to optimize the PA systems [14–24]. With the development of the laser technique, high-power lasers such as quantum cascade lasers (QCLs) [14,15] and tunable distributed feedback (DFB) lasers cascaded with an erbium-doped fiber amplifier (EDFA) [16,17] are used as an excitation light source, in order to enhance the PA signals. Moreover, novel strategies of intracavity PAS have been presented to fully utilize the intracavity laser power [18–20]. For further improving the amplitudes of PA signals, high-sensitivity fiber-optic acoustic sensors [21,22] and quartz tuning forks [23,24] take the place of conventional microphones as sound wave detectors. However, there are few studies on the improvement of the PA cell constant.

The PA cell is the core unit in a PAS system where the periodic light absorption of gas molecules is converted into acoustic pressure waves. The PA cell constant, which represents the energy transformation capacity from light energy to acoustic energy, determines the performance of a PA cell. According to the working mode of acoustic waves, the PA cell includes a resonant PA cell and a non-resonant PA cell [25]. The resonant PA cell where PA signals form stationary waves has a high sensitivity for trace gas detection. In recent years, the H-type first longitudinal resonant PA cell is used frequently because of its good match with axially-symmetric beams, good match with axially-symmetric PA fields, and easy processing [26]. Furthermore, some differential H-type PA cells were used in order to improve the performance of PA system [27–30]. Yin *et al*. designed a differential PA cell, which consists of two identical cylindrical channels performing as two acoustic resonators [27]. The symmetric double resonator construction of the PA cell constitutes a differential PA cell, which resembles the well-known differential Helmholtz resonator. The differential PA cell, together with a 3.5 W blue multimode diode laser, constitutes a nitrogen dioxide (NO_{2}) sensor system with a detection limit of 54 parts per trillion (ppt) for a 1-s averaging time. With the same miniaturized differential PA cell and an interband cascade light emitting device, a minimum detection concentration level of 3.6 parts per million (ppm) for methane (CH_{4}) was achieved [4]. Liu *et al*. demonstrated a multi-gas sensor based on a multi-resonator PAS. The PA cell included three acoustic resonators operating at different resonant modes, corresponding to water (H_{2}O), CH_{4} and carbon dioxide (CO_{2}), respectively. Experimental results showed that the minimum detection limits were 1.3 ppm for H_{2}O, 4.4 ppm for CH_{4}, and 140 ppm for CO_{2} [28]. However, if the radius and length of the resonator is constant, the PA cell constants of conventional H-type longitudinal resonant PA cells are difficult to be increased, which hampers the further development of performance for PAS system. Meanwhile, there are two buffers at both ends of the resonator, and therefore the H-type PA cell has a large volume, which increases the equilibration time of the measured gases. Furthermore, in order to be cooperative with the acoustic detector, there must be an opening in the central position of the resonator for the H-type resonant PA cell, which makes it difficult to fabricate the PA cell.

In this paper, we present a novel T-type half-open resonant PA cell. Compared with the conventional H-type longitudinal resonant PA cell, the T-type longitudinal resonant PA cell has a higher PA cell constant, a faster response time and a simpler manufacturing process. The T-type half-open resonant PA cell, together with a distributed feedback (DFB) laser, and a fiber-optic acoustic sensor, constitutes a PAS system for trace gas analysis. The system was successfully used for acetylene (C_{2}H_{2}) gas detection and achieved a low concentration detection limit.

## 2. T-type PA cell design and performance test

The schematics of the proposed T-type half-open longitudinal resonant PA cell and conventional H-type longitudinal resonant PA cell are shown in Fig. 1. The H-type longitudinal resonant PA cell consists of an identical cylindrical resonator and two buffer volumes at both ends of the cylindrical resonator. The acoustic sensor is placed on the wall in the middle of the resonator to detect the PA pressure. In contrast, the proposed T-type has just one buffer volume, and the acoustic sensor is placed at one end of the resonator, therefore the resonator has an easier fabrication process without an opening.

The heat produced by the absorption of light acts as a source for the generation of sound that can be described by the acoustic pressure *p(r, t)*. Ignoring the energy losses due to heat conduction and viscosity, the wave equation of the acoustic pressure changes *p(r, t)* is given as [11,29]:

*v*is the speed of sound in the sample gas;

_{$H(\overrightarrow{r},t)$}is the heat produced by the absorption of light per unit volume.

*γ*is the ratio of specific heats of the gas at constant pressure

*C*to that at constant volume

_{p}*C*.

_{v}*and*

_{$\overrightarrow{r}$}*t*represent the position and time, respectively.

In order to solve the Eqs. (1), taking the Fourier transform of both sides, the Fourier transform of Eqs. (1) is given by [11,31]:

*ω*is the angular frequency. The solution for

_{$p(\overrightarrow{r},\omega )$}is expressed as [29]:where

_{${p}_{j}(\overrightarrow{r})$}and

_{${A}_{j}(\omega )$}are the normal mode solutions and the mode amplitudes.

_{${p}_{j}(\overrightarrow{r})$}is determined by the following [29]: where

*k*. For the proposed T-type longitudinal PA cell, a cylindrical coordinate

_{j}= ω_{j}/v*is used; the*

_{$\overrightarrow{r}$}= r(r,θ,z)*z*axis coincides with the axis of the cylinder. The left-hand side of the resonator is at

*z*= 0, and the right-hand side is at

*z*= L. Then, the acoustic mode

_{${p}_{j}(\overrightarrow{r})$}and resonant frequency

*f*can be solved from Eqs. (4) and (5) [32]:

_{j}*R*and

*L*are the radius and length of the resonator, respectively;

*j = (nmq)*,

*n*,

*m*and

*q*are the radial, azimuthal, and longitudinal mode numbers, respectively;

_{${\alpha}_{mn}$}is the (

*n*+ 1)th root of equation

_{${\left[d{J}_{m}\left(\frac{\pi {\alpha}_{mn}}{R}r\right)/dr\right]}_{r=R}=0$};

*J*is

_{m}*m*th order Bessel function.

For a first-order longitudinal resonant PA cell, *m* = *n* = 0, *q* = 1, _{${\alpha}_{mn}$} = 0, _{${p}_{j}(\overrightarrow{r})$} = _{${p}_{00q}(\overrightarrow{r})$}, therefore *f _{001}* and

_{${p}_{001}(\overrightarrow{r})$}can be expressed as:

If *z* = 0, the acoustic mode _{${p}_{001}(\overrightarrow{r})$} = 1. Therefore, the position where the acoustic sensor is located, is the antinode of the resonant acoustic waves; If *z* = L, the acoustic mode _{${p}_{001}(\overrightarrow{r})$} = 0. Therefore the position where is the junction of the resonator and the buffer volume, is the node. While for the traditional H-type resonant PA cell, the first-order resonant frequency *f _{001H}* is determined by [29]:

Comparing Eqs. (8) and (10), for the same length *L* of the resonator, the first-order resonant frequency of T-type resonant PA cell is half of the H-type’s.

For the first-order longitudinal resonant PA cell, the PA cell constant *F* can be expressed as [30]:

*V*is the volume of the resonator, and

*Q*is the Q factor of the PA cell, which is given by [33,34]:where

*η*is the viscosity constant,

*ρ*the gas density,

*κ*the thermal conductivity of the gas, M the molar mass, and

*C*the specific heat of the gas at constant pressure. Therefore the Eqs. (11) is changed to:

As shown in Eqs. (13), if radius and length of the resonator is constant, the PA constant *F* is inversely proportional to the square root of the first-order resonant frequency $\sqrt{f}$. Therefore, the proposed T-type resonant PA cell has a higher PA constant.

Because the resonant PA cell has end effects, the length *L* of the two kinds of resonant PA cells have to be amended as [35]:

The inner diameter and length of the resonator are 8 mm and 120 mm. The inner diameter and length of the buffer are 20 mm and 60 mm. Therefore, the theoretical first-order resonant frequencies of T-type and H-type resonant PA cells are 707 Hz and 1377 Hz, respectively.

A 3D finite element model using COMSOL Multiphysics was constructed to evaluate the PA field distributions at the first resonant frequency of the T-type and H-type resonant PA cells. As shown in Fig. 2, for the T-type resonant PA cell, the end of the resonator is the antinode of the resonant acoustic waves, where the maximum acoustic pressure exists; while for the conventional H-type resonant PA cell, the antinode of the resonant acoustic waves is in the middle of the resonator, which verifies the theoretical analysis.

Figure 3 shows the frequency responses of the T-type and H-type resonant PA cell. As shown in the inset of Fig. 3, the first-order resonant frequency of the H-type resonant PA cell is 1402 Hz, which has been tested in our previous work [36]. In order to verify the theoretical analysis results, the first-order resonant frequency of the T-type resonant PA cell was tested experimentally. The external acoustic pressure was fixed at the intensity of 1 Pa by a sound generator and a referenced microphone, and the frequency responses were measured by changing the acoustic frequency from 100 Hz to 1600 Hz. The Fabry-Perot (F-P) acoustic sensor based on a 3 μm thick titanium film was fixed at the end face of the resonator. The resonant frequency of the 3 μm thick titanium film was about 2200 Hz. With the same resonator and buffer, the first-order resonant frequency of T-type resonant PA cell was measured to be 748 Hz, which are close to the theoretical results.

## 3. PA system and experimental results

The schematic diagram of the experimental system based on PAS is shown in Fig. 4. It is comprised of a computer, a DFB laser, an erbium-doped fiber amplifier (EDFA), a cantilever microphone, a T-type PA cell and a demodulation system of the cantilever microphone. The central wavelength of the DFB laser, which is used as the PA excitation source, is 1532.83 nm. The ramp voltage and the sinusoidal waveform voltage were added to drive the DFB laser. The sinusoidal modulation frequency was half of the resonant frequency of the PA cell. The power of the near-infrared laser light was amplified to be 500 mW by the EDFA (AEDFA-27-B-FA, Amonies). The laser light was collimated into the T-type first-order longitudinal resonant PA cell. To improve the effective excitation power, the laser light was reflected by a gold plated mirror. There is an air inlet and an air outlet on the PA cell. When the system operates, the two inlets were turned off to assure airtightness of the PA cell. The gas absorption-induced PA signal was detected by a cantilever microphone and was placed at one end of the resonator. A detailed description of the cantilever microphone and the demodulation system can be found in [37]. The whole measurement process was controlled by a LABVIEW based computer program. The H-type first-order longitudinal resonant PA cell was used in this system for comparison. The whole experimental process was kept at room temperature and atmospheric pressure.

In general, the microphone operates better in a relative flat area of the spectrum. Therefore, the thickness of the cantilever is 10 μm, and the sizes of the cantilevers are 2.9 mm × 1 mm and 2 mm × 1 mm, respectively, which are matched with the T-type and H-type PA cells. Figure 5 shows the frequency responses of the two cantilever microphones. The first-order resonant frequencies are 1150 Hz and 1858 Hz, respectively. The sensitivity of the cantilever microphone matched with T-type PA cell is 241.5 mV/Pa at the frequency of 748 Hz, which is the first-order resonant frequency of the T-type PA cell. The sensitivity of the other cantilever microphone matched with H-type PA cell is 256.7 mV/Pa at the frequency of 1402 Hz, which is the first-order resonant frequency of the H-type PA cell.

For the T-type PA cell based trace gas detection experiment, acetylene with different concentrations has been tested. A gas mixing system, consisting of two mass flow controllers (D07-19, SevenStar), was used to generate a C_{2}H_{2}/N_{2} gas mixture with different concentrations. The PA signals were measured with the wavelength modulation and second-harmonic detection methods. The wavelength of the DFB laser was tuned from 1532.77 nm to 1532.89 nm with tuning steps of 2 pm, and the measurement time of one period was 60 s. The PAS signals as a function of C_{2}H_{2} concentrations are plotted in Fig. 6. The responsivities of the system for C_{2}H_{2} detection are estimated to be 4.47 mV/ppm and 3.67 mV/ppm by linear fitting, respectively, which corresponded to the proposed T-type and conventional H-type PA cell. The PA signal generated in the T-type PA cell is about 1.22 times the PA signal of the H-type PA cell at the same concentration of C_{2}H_{2}. Because the PA signal is proportional to the sensitivity of microphone, the theoretical ratio value is _{$241.5/256.7\times (\sqrt{1402}/\sqrt{748})\text{=}1.30$}, which is similar to 1.22.

The background noise was analyzed by filling the PA cell with pure N_{2}, as shown in Fig. 7. The output of the lock-in amplifier was monitored with both the DFB laser and EDFA turned on. The measurement time was 60 s for one period of wavelength modulation. From Fig. 7, the voltage noise levels (1σ) can be calculated to be 3.12 μV and 3.07 μV, respectively. With the responsiveness of 4.47 mV/ppm and 3.67 mV/ppm, the gas detection limits for C_{2}H_{2} can be estimated to be 0.70 ppb and 0.84 ppb, which corresponded to T-type and H-type PA cells. The proposed T-type resonant PA cell based trace gas detection system has a lower detection limit. The peak power output of the EDFA used in this experiment is 500 mW, therefore it will be feasible to further decrease the gas detection limit by increasing the output power of the excitation light source. Furthermore, an acoustic resonant enhancement will enhance the detected PA signals.

For the conventional H-type resonant PA cell, the gas circulates because of the blocking of cell wall, before entering the resonator. Therefore, it increases the response time for trace gas detection. While for the proposed T-type resonant PA cell, the measured gas enters the resonator through the inlet valve directly, and then exists. To prove the advantage of a faster response time, comparative experiments of cleaning time for the two kinds of PA cells were performed. First, the PA cells were filled with C_{2}H_{2} at the concentration of 3 ppm. Secondly, the high purity N_{2} gas was sequentially injected in the PA cells and the flow rate of the mass flow controller was set at 2 standard cubic centimeter per minute (SCCM). After one minute, the valves were closed and the N_{2} gas was stopped. Then the stabilized PA signals were measured and recorded. After that, the N_{2} gas was continued to be injected into the PA cells for one minute and the PA signal was recorded. The process was repeated until the measured PA signals were no longer decreasing. Figure 8 shows the cleaning time comparison of the two kinds of PA cells. For the T-type resonant PA cell, the PA signals remain unchanged after the N_{2} gas was injected for six minutes. Hence, the cleaning time of T-type resonant PA cell is about six minutes. In contrast, the H-type PA cell was cleaned for 11 minutes. Therefore, the proposed T-type resonant PA cell has a faster response time.

## 4. Conclusion

In conclusion, we proposed and experimentally demonstrated a novel T-type half-open resonant PA cell. The proposed T-type resonant PA cell has one buffer volume, and the fiber-optic acoustic sensor is placed at one end of the resonator, so that the resonator is easier to fabricate without an opening. The first-order resonant frequencies of the proposed T-type PA cell and conventional H-type PA cell are 748 Hz and 1402 Hz, respectively, with the same resonator whose inner diameter and length are 8 mm and 120 mm. The PA constant is inversely proportional to the square root of the first-order resonant frequency. Therefore, the proposed T-type resonant PA cell has a higher PA constant. The T-type resonant PA cell was used in C_{2}H_{2} gas detection system based on PAS. The PAS system is comprised of a computer, a DFB laser, an EDFA, a T-type PA cell, a cantilever microphone and its demodulation system. The PA signals were measured with the wavelength modulation spectrum and second-harmonic detection methods. The wavelength of the DFB laser was tuned from 1532.77 nm to 1532.89 nm with tuning steps of 2 pm, and the measurement time of one period was 60 s. Experimental results show that the second harmonic amplitude of the PA signal is proportional to the concentration of C_{2}H_{2} for the range of 0-3 ppm and the sensitivity is measured to be 4.47 mV/ppm, which is 1.22 times the PA signal of the H-type PA cell. The minimum detectable limit of C_{2}H_{2} is calculated to be 0.70 ppb (SNR = 1). In contrast, the traditional H-type PA cell based C_{2}H_{2} detection system has a minimum detectable limit of 0.84 ppb for C_{2}H_{2}. Furthermore, the high purity N_{2} gas was used to clean the PA cell filled with C_{2}H_{2} of 3 ppm. The T-type PA cell was cleaned up for six minutes, while the H-type PA cell needed 11 minutes. Therefore, the proposed T-type resonant PA cell has a faster response time. In summary, compared with the conventional H-type longitudinal resonant PA cell, the T-type longitudinal resonant PA cell has a higher PA cell constant, a faster response time and a simpler manufacturing process.

## Funding

National key research and development program of China (2016YFC0200600); National Natural Science Foundation of China (61705030); Fundamental Research Funds for the Central Universities (DUT18RC(3)035, DUT18RC(4)040, and DUT18JC22), State grid corporation of China (521205190014.

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