## 5 Detection of Pure Methane, Ethylene, and Ethane  
The photoacoustic sensor was calibrated under the optimized experimental conditions described above. The results show that the line broadening is so pronounced at atmospheric  
Figure 6: (**a**) 1f and (**b**) 2f signals of the three analytes in the full dynamic range of the ICL current (50 to 100 mA). Figure 7: (**a**) First harmonic signals of 50 ppm methane under atmospheric pressure obtained at different phase angles; (**b**) cosine function fitting of the signal at an injected current of 62.57 mA. pressure that the three absorption peaks/lines of methane are no longer distinguishable (Figure 6). At a current of \(I\) = 64.81 mA, the laser emission wavelength corresponds to the absorption of CH\({}_{4}\) at 3345.68 nm, and the laser currents of \(I_{1}\) = 62.35 mA and \(I_{1}\)\({}^{\prime}\) = 67.81 mA correspond to the two peaks of its first harmonic. Because the absorption of CH\({}_{4}\) at current \(I_{1}\)\({}^{\prime}\) has a large overlap with the absorption of C\({}_{2}\)H\({}_{4}\), and the signals cancel each other, the signal at a current of \(I_{1}\) is selected for the extraction of methane concentration. According to the data in the HITRAN database (Figure 1), C\({}_{2}\)H\({}_{4}\) does not have a relatively sharp peak with high line strength in this band, but exhibits a broad band, and its first harmonic presents an asymmetric line type. C\({}_{2}\)H\({}_{6}\) has two absorption peaks at 3344.40 nm and 3348.19 nm, and the former has a weaker absorption intensity. To obtain a longer laser wavelength in ICL, a larger injected current is needed, and as a result, the laser power output is higher and the obtained DHR photoacoustic signal is stronger. Hence, detecting C\({}_{2}\)H\({}_{6}\) near 3348.19 nm is a better choice [22]. To reduce cross-interference, the detection current of C\({}_{2}\)H\({}_{4}\) is selected as \(I_{2}\) = 73.88 mA, and the detection current of C\({}_{2}\)H\({}_{6}\) is selected as \(I_{3}\) = 88.23 mA. For ethylene, the standard substance 401 ppm gas was used as the sample gas, and high-purity nitrogen was used as the dilution gas. Figure 9 shows the ethylene concentration gradient scan from 5 to 85 ppm. At the selected ethylene detection laser current, \(I_{2}=73.88\) mA, the signal values of different concentrations are taken to draw the working curve. The data in the figure show that the signal response values of ethylene under this laser current have a good linear relationship, and the responsivity of the photoacoustic signal to the gas concentration is \(-1.778\) mV/ppm. The Allan bias analysis shows (Figure 9c) that the lowest detectable concentration for ethylene detection is 252 ppb for an integration time of 2 s.  
For ethane, the standard 207 ppm gas was used as the sample gas, and high purity nitrogen was used as the dilution gas. Figure 10 shows the ethane concentration gradient scan from 2 to 90 ppm. At the selected ethane detection laser current, \(I_{3}=88.23\) mA, the signal values of different concentrations are taken to draw the working curve. The data in the figure show that the signal response values of ethane under this laser current have a good linear relationship, and the responsivity of the photoacoustic signal to the gas concentration is \(-13.78\) mV/ppm. The Allan deviation analysis shows (Figure 10c) that the lowest detectable concentration for ethane detection is 33 ppb for an integration time of 2 s.  
Figure 9: (**a**) The 1f signals of ethylene (5 to 85 ppm) at ambient pressure with the laser current in 53–100 mA; (**b**) Linearity of the 1f signal of ethylene obtained at \(I_{2}=73.88\) mA; (**c**) Continuous measurement 95.0 ppm ethylene; (**d**) The Allan deviation analysis. In summary, the above results show that ethane has the highest responsivity and ethylene has the lowest responsivity. Although the absorption intensity of methane is stronger than ethane, the absorption cross section of methane is far lower than that of ethane.