## 3 Results
### Calibration Curve, Sensitivity, and Detection Limits  
The excitation laser current was tuned to an NH\({}_{3}\) absorption line and wavelength modulation (WMS) was implemented by directly modulating the laser using a sinusoidal signal from the lock-in amplifier with a frequency of 3400 Hz, which is half the frequency of the main resonant mode (_fr_/2). This signal was connected to the laser driver, which allowed for an external modulation connection with a modulation coefficient of 150 mA/V. Subsequently, the acquired signal was demodulated in the second harmonic using the lock-in amplifier, thus performing _2f_-WMS detection. The modulation amplitude was varied in a range between 20 mV and 100 mV to find the optimal amplitude that maximizes the central peak value and obtains the best spectral response. Figure 9a shows the detected spectra of the _2f_-WMS signal for three different amplitudes, while Figure 9b shows the amplitude value for the central peak (Amplitude 1) and the difference between the main peak and the first peak on the left (Amplitude 2) for 10 different amplitude values. In this way, the optimal modulation amplitude was identified as 60 mV [34].  
Figure 7: (**a**) Diagram of the installation of the three sensors perpendicular to the optical beam. (**b**) Resonant modes within the cell identified by the three microphones parallel to the optical beam.  
As mentioned above, starting from the certified concentration of 5000 ppm NH\({}_{3}\):N\({}_{2}\), different concentrations of NH\({}_{3}\) were obtained, from 200 ppm to 5000 ppm, using a gas mixer and maintaining a constant flow throughout the measurement of 60 mlm. For each concentration, several spectral sweeps of the NH\({}_{3}\) absorption line were recorded. Representative _2f_-MPC-PAS scans are shown in Figure 10a. The average peak signal values were plotted against NH\({}_{3}\) concentration. The data set together with the best linear fit, representing the calibration curve of the NH\({}_{3}\) sensor, is shown in Figure 10b. A coefficient of determination (R2) of 0.987 is obtained, confirming the linearity of the sensor over this range.  
Finally, to estimate the noise, a laser wavelength sweep was performed in the measurement range between 84.9 and 103 mA, as shown in Figure 11. The noise level was determined from the signal obtained with the gas cell filled with N\({}_{2}\) only. This signal was taken every second for 60 s. The data set was then analyzed, and the standard deviation of the noise sample (1\(\sigma\)) was determined to be 5.36 \(\times\) 10\({}^{-7}\) V. The minimum detection limit (SNR = 1), taking into account the standard deviation of the noise (1\(\sigma\)), was estimated at 770 ppb, using the ratio between the standard deviation of the background noise and the sensitivity of the system (slope of the calibration curve in Figure 10b). Consequently, the corresponding normalized equivalent absorption coefficient (NNEA) for NH\({}_{3}\) was 1.07 \(\times\) 10\({}^{-8}\) W cm\({}^{-1}\) Hz\({}^{-1/2}\), obtained with a bandwidth of 0.26 Hz (for a time constant  
Figure 8: Detail of the main resonance mode for sensors M1 and M2.  
Figure 9: (**a**) _2f_-WMS photoacoustic signal for different modulation amplitudes of the same NH\({}_{3}\) absorption lines. (**b**) _2f_-WMS photoacoustic signal of the main peak amplitude (Amplitude 1) and the difference between the main and secondary peaks on the left (Amplitude 2) as a function of modulation amplitude. All measurements were made with a mixture of 5000 ppm NH\({}_{3}\) in N\({}_{2}\) at atmospheric pressure and room temperature.  
of 0.3 s) and an effective power of 30 mW, which was calculated by considering the ratio between the incident power and the output power measured by the reference photodetector.