Theory. Figure 1 shows the basics of opto-acoustic resonance for PAS. The core gas sensing element consists of an optical resonator, an acoustic resonator, and an acoustic transducer, which are arranged in a coupled configuration. Indeed, when the optical frequency of the incident laser is in resonance with a longitudinal cavity mode of the optical resonator, a standing optical wave is formed between the resonator mirrors. A high-finesse optical resonator can significantly build up the laser power, by several orders of magnitude [25], directly enhancing the photoacoustic signal which scales linearly with the laser power. The laser intensity is modulated at the same resonance frequency as the acoustic resonator. A specifically designed one-dimensional longitudinal tube can be used to amplify the acoustic signal by forming a standing acoustic wave inside it. Any types of acoustic transducers can be used to detect the amplified acoustic wave. In this work, we use both a quartz tuning fork (QTF), resonant at the same frequency as the acoustic resonator, and an electret microphone for demonstration. As shown in Fig. 1, the QTF locates nearby the antinode of the standing acoustic wave, which is generated by the acoustic resonator composed of two stainless-steel tubes placed at the opposite sides of the QTF [26]. The other photoacoustic sensor configuration using an electret microphone is described in the Supplementary Note 3.
The frequency-dependent photoacoustic signal (S) at its resonant frequency f is given by:
![](data:image/jpeg;base64,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where b is the laser power buildup factor, g is the acoustic wave enhancement factor, K is the sensor constant, Win is the incident laser power, λ is the laser wavelength, αeff(λ) is the effective absorbance by the analyte, τ(P) is the relaxation time at the gas pressure P, and ε is the radiation-to-sound conversion efficiency [27], which depends on f and τ. Note that the factor g is independent of laser power but is related to the geometry, to the material, and to the Q-factor of the acoustic resonator, as well as to the frequency of sound waves [28]. The power buildup factor b is determined by the finesse of the optical resonator, which needs to be properly selected so that a wide linear dynamic range and a high sensitivity can be simultaneously obtained (see Methods).
Experimental setup. The schematic of the PAS sensor is shown in Fig. 2. An external cavity diode laser (ECDL) is used to detect the P(11) line of C2H2 at 1531.59 nm. The ECDL is phase modulated by an electro-optic modulator (EOM) at 20 MHz and locked to the optical resonator using the Pound-Drever-Hall (PDH) method [29]. Details of the application of the PDH method to PAS can be found in [24]. In this work, the current and piezo transducer (PZT) feedback loops are both used for a more robust locking performance. Each mirror of the optical resonator has a radius of curvature of 150 mm and reflectivity of 99.923% (finesse 4078) at the laser wavelength, as measured by cavity ring-down (see Supplementary Note 1). Compared with other cavity-enhanced absorption spectroscopic methods [6,10], the optical resonator used here for the opto-acoustic resonance features a much shorter length (60 mm in this work). Two mode matching lenses (f1 and f2) are used to maximize the coupling efficiency (84%) between the laser and the optical resonator (see Supplementary Note 2). With a maximum incident laser power of 300 mW, the intracavity optical power is boosted to 264 W in this work (see Methods).
The intracavity laser beam passes through the acoustic resonator, consisting of two stainless-steel tubes (inner diameter 1.3 mm, length 23 mm), and does not touch any surface. The central axis of the acoustic resonator is about 1.2 mm below the top of the QTF prongs, thus optimizing the piezoelectrical conversion efficiency [15]. The two tubes are placed at a distance of ~60 μm from the QTF, so that it lies near the antinode of the acoustic wave and leaves its Q-factor unaffected. The beam waist (340 μm in diameter) is located between the two prongs of the QTF, which has a resonant frequency of 7.2 kHz and a Q-factor ~8000 (gas pressure 760 Torr) [15]. Photoacoustic gas sensors using QTF as an acoustic transducer have been previously developed for detecting many different gas species [15-17]. The optical resonator, the acoustic resonator and the QTF are all enclosed inside a chamber. A high-speed lithium niobate optical switch is used to chop the laser beam at the same frequency as the resonant frequency of the QTF. The piezoelectric current from the QTF is collected by a trans-impedance amplifier and then amplified by a low-noise voltage preamplifier. Finally, a lock-in amplifier with a detection bandwidth of 1 Hz is used to demodulate the first harmonic signal (1f) at the sensor output.
Double standing wave enhancement. To evaluate the enhancement effects due to the integrated acoustic and optical resonators, the PAS-1f signal of the C2H2 line at 1531.59 nm is measured under three different configurations. Figure 3 compares the typical PAS-1f signal measured using a bare QTF (2% C2H2), a QTF with the mere acoustic resonator (0.1% C2H2), and a QTF with the complete opto-acoustic resonator (1 ppm C2H2). Note that different C2H2 concentrations are used for these three configurations because of their quite different sensitivity. All the experiments are performed at the same incident laser power of 12 mW, lock-in detection bandwidth of 1 Hz, and gas pressure of 760 Torr. After normalization by the gas concentration, a comparison of Fig. 3(a) and Fig. 3(b) shows that the acoustic resonator enhances the PAS-1f signal by 175 times. Besides, the optical resonator provides another enhancement factor of 980, as emerging from a comparison of Fig. 3(b) and Fig. 3(c). Hence, the combined opto-acoustic amplification provides an overall enhancement of the PAS signal by a factor of 105 via the double standing wave effect.
Ultra-sensitive gas detection. Figure 4 shows the PAS-1f signal measured by the photoacoustic sensor for an incident optical power of 12 mW. The measurement is performed at 760 Torr for different C2H2 concentrations (100 ppb and 10 ppb in nitrogen balance) and high-purity nitrogen (99.999% purity) when the laser wavelength is tuned from 1531.32 nm to 1531.75 nm. The peak values at 1531.59 nm are 4.05 mV (100 ppb C2H2) and 0.68 mV (10 ppb C2H2), respectively. Note that the background signal is contributed by the thermoelastic effect due to unwanted absorption at the optical window and resonator mirror [30]. This background signal has not been subtracted from the PAS-1f signal shown in Fig. 4. Interestingly, due to the excellent signal-to-noise ratio, a neighboring water line near 1531.37 nm emerges, as shown in Fig. 4(b). This is probably due to residual water in the gas chamber after the desiccation process (see Methods). Our hypothesis is confirmed by repeating the measurement with pure nitrogen (water vapor < 0.3 ppm) shown in Fig. 4(c). To reduce the measurement uncertainty, a multi-spectral fitting method, with prior knowledge of infrared spectra from the HITRAN database [31], is implemented. Hence, the background signal is automatically eliminated during the fitting procedure.
The relationship between the PAS-1f signal and incident laser power is also investigated. Figure 5(a) compares the PAS-1f signal at 1 ppb C2H2 under two different incident power levels (12 mW and 300 mW). The peak value of the PAS-1f signal is increased by a factor of about 22.5 when the incident laser power is increased from 12 mW to 300 mW (a factor of 25). The slight deviation of the enhancement factor between laser power and PAS signal is due to the variation of the optical coupling efficiency. By repeating the measurement at 100 ppb C2H2, Fig. 5(b) shows the variation of the PAS-1f amplitude with the incident optical power. The sensor signal increases almost linearly (0.25 mV/mW) with the incident power. In contrast, the noise level remains almost unchanged over the entire power range, as shown in Fig. 5(b) (1-σ standard deviation of N2 over 120 s). This makes this set-up very promising to further increase detection sensitivity by simply increasing the incident laser power.
Test of dynamic range and detection limit. The linear response of the sensor is tested at the pressure of 760 Torr by filling the gas chamber with different C2H2/N2 mixtures. Fig. 6 shows the background-subtracted PAS-1f amplitude as a function of C2H2 concentration, varying in a 1 ppb-500 ppm interval. The sensor shows a very good linear response with a slope of 36.4 μV/ppb and an R-square value of 0.99 from 1 ppb to 50 ppm. However, the sensor deviates from the linear response at higher C2H2 concentrations due to the apparent degradation of optical finesse of the optical resonator.
To evaluate the long-term stability and the minimum detection limit, the Allan–Werle deviation analysis is conducted by measuring nitrogen with the results shown in Fig. 7. The noise equivalent concentration (NEC) is determined to be 5.1 ppt (unity for signal-to-noise ratio) at an integration time of 1 s. At an incident optical power of 300 mW and a detection bandwidth of 1 Hz, we obtain a normalized noise equivalent absorption coefficient (NNEA) of 1.7×10-12 Wcm-1Hz-1/2 (see Methods). The NEC can be improved to 0.5 ppt at a longer integration time of 300 s, leading to a noise equivalent absorption (NEA) of 5.7×10-13 cm-1. As a result, the proposed photoacoustic gas sensor achieves a linear dynamic range of 1.0×108.
To verify the versatility of this technique, we also develop another photoacoustic sensor by using a conventional longitudinal acoustic resonator with buffering volumes (Q-factor 25), an electret microphone, and a longer optical resonator (80 mm) with the same finesse (see Supplementary Note 3). The microphone-based sensor can be easily aligned along the optical path and a similar performance in terms of sensitivity and dynamic range is demonstrated, as compared to the previous configuration.
The dynamic stability of the sensor is also important for applications requiring continuous gas sampling. This is evaluated by operating the gas sensor when continuously filling C2H2 gas samples into the gas chamber. Our sensor behaves well, without any interruption, during the gas filling and flow rate changing processes (see Supplementary Note 4).