## 4 Experimental Sensing Setup
### Tunable Fiber Laser  
Here, a tunable laser based on an erbium doped fiber ring cavity is utilized. Basically, this tunable laser is formed by a ring cavity in which a bulk silicon wafer of 85 \(\upmu\)m thickness is used as a spectral selective filter [25]. Hence, the wafer acts as a Fabry-Perot interferometer (FPI) and therefore its reflection pattern can be shifted by varying the refractive index of silicon. This can be achieved by taking advantage of the thermo-optical properties of silicon [25]. Consequently, this allowed us to tune the laser emission wavelength to match one ro-vibrational absorption line of the target molecule. In our case, we matched the laser emission with the ro-vibrational line of C\({}_{2}\)H\({}_{2}\) occurring at 1532.8302 nm at atmospheric pressure [24]. Furthermore, in the laser cavity a variable optical attenuator (VOA) was used to suppress emissions in the region of 1550 nm. Here, the laser fine tuning mechanism depends directly on the silicon wafer that is acting as wavelength selective filter and it can be tuned by changing its temperature. Additionally, the VOA induces a coarse shifting and can help to select different wavelength regions. For the experiments carried out in this work, the VOA remained fixed. For dual path correlation spectroscopy measurements, it is necessary that the laser wavelength must remain stable over the time, otherwise considerable errors will be obtained. For instance, in Figure 5a it can be observed, from simulation results, that the depth of modulation error rapidly increases as the wavelength deviate a few picometers from the reference wavelength. Hence, the gas line absorption is acting as an extremely narrow suppression band filter and, therefore, if the laser wavelength slightly shifts, the signal monitored by the detectors will change in a considerable way. Therefore, this issue allowed us to indirectly assume that the laser line is wavelength locked by monitoring that the detectors output remains fixed over the time. In this way, we characterized that by keeping the silicon wafer constant such that the laser wavelength was locked. In our sensing arrangement, the wafer temperature was varied by means of a thermo-electric cooler (TEC) to reach the desired wavelength. Moreover, once the wavelength is matched, the Si wafer temperature must be kept stable over the time. In order to achieve this temperature stability, it was necessary to drive the TEC with a proportional-integral derivative (PID) control program that was implemented in LabVIEW software. By driving the TEC with this PID controller, it was possible to maintain the temperature of the Si wafer as highly stable, with a standard deviation of just 0.02 K. This represents that the laser wavelength was fixed to 1532.8302 pm with an estimated standard deviation of approximately 0.12 pm. These measurements were taken over a period of 3 h (Figure 5b) and show that the laser is suitable  
Figure 4: Hybrid C\({}_{2}\)H\({}_{2}\) sensor setup based on the LL-TLAS and NDS correlation spectroscopy techniques. for this sensing application. The measured spectral profile of the laser emission \((L_{M})\) is shown in Figure 6a, where it can be appreciated that it has a FWHM of approximately 16 pm, which is thinner than the ro-vibrational line of C\({}_{2}\)H\({}_{2}\) occurring at 1532.8302 nm at atmospheric pressure [24]. In general the expected \(D_{M}\) errors at the sensor output due to laser wavelength shifting (Figure 5a) can be explained by the fact that the laser width is narrower than the absorption line width. Hence, if the laser spectrally shifts, the power will rapidly increase following the shape of the gas absorption line. Therefore, the system tolerance to the laser wavelength shifting will also be affected by the pressure at the gas cell since it modifies the molecule absorption line widths. In our case we are characterizing the sensor response at atmospheric pressure.