## 2 Experimental Apparatus and Measurement Principle  
CEAS is essentially a direct absorption spectroscopy technology that follows the Beer-Lambert law. By direct measurement of the optical cavity transmitted light field, the absorption coefficient of gas is measured in the cavity bonding Equation (1):  
\[I(\lambda)=I_{0}(\lambda)\exp[-\alpha(\lambda)L] \tag{1}\]  
where \(I(\lambda)\) denotes the signal of transmitted light; \(\lambda\) denotes the light frequency; \(I_{0}(\lambda)\) represents the incident light intensity; and \(L\) is the effective absorption path. \(\alpha\) represents the gas absorption coefficient, which can be described as in Equation (2):  
\[\alpha(\lambda)=CNS(\lambda)\text{g}(\lambda-\lambda_{0}) \tag{2}\]  
where \(C\) represents the concentration of the absorbing gas; \(N\) represents the molecular number density; \(S\) represents the spectral line intensity; and \(g(\lambda-\lambda_{0})\) is the normalized line profile. CEAS realizes the multiplication of effective absorption paths (100-10,000 times), depending on the relaxation effect of the ultra-low loss optical cavity. The detection sensitivity and limit of trace gas concentration can be improved greatly. As an improvement of CEAS, OF-CEAS can effectively increase the laser injection rate of the high finesse optical cavity. In OF-CEAS, a portion of the resonance light returned to the laser. When the feedback optical field has been matched in phase and feedback rate, the semiconductor laser's linewidth can be effectively narrowed, and the laser frequency can be locked with the resonance frequency of the high finesse optical cavity [14; 15; 16]. As a result, the transmitted light intensity and sensitivity of the cavity will be significantly improved compared to conventional CEAS [16]. A distributed feedback semiconductor laser (SWLD-151210P22-09, Allwave Lasers, Xi'an, China) was adopted as the light source for the system. As shown in Figure 1, the working state of the distributed feedback laser is controlled by a high precision temperature driver and current driver. The light from the distributed feedback laser is injected into a single-mode polarization-maintaining (PM) fiber. The pigtail output is connected with an optical fiber coupler (50:50, 1550 nm Center Wavelength). The two output ports of the fiber coupler are separately linked to the adaptable fiber collimator and the optical detector PDA4 (PDA10 CS-EC, Thorlabs, Newton, NJ, USA). The cavity is a U-shaped cavity consisting of three arms and two 45\({}^{\circ}\) folding angles. The length of L1 and L3 is 170 mm, the length of L2 is 132 mm and the circumference is 472 mm. The cavity body used is glass-ceramic with an ultralow expansion coefficient (\(\sim\)10\({}^{-8}\)/\({}^{\circ}\)C). The cavity includes four mirrors made of fused quartz (diameter is 25 mm). Among them, the mirrors M2 and M3 are plane mirrors, and the mirrors M1 and M4 are spherical mirrors with a radius of curvature of 2 m. An ultra-high reflectivity film (diameter is 10 mm, R \(>\) 99.99% at 1530 \(\pm\) 30 nm) lies in the central region of the mirror. Piezoelectric ceramic transducer (PZT) for the cavity length scanning is installed behind the spherical mirror M4. Compared with the V-shaped cavity, the design of the U-shaped cavity can not only realize the optical feedback effect, but also collect the transmitted light intensity signal by setting a photodetector (PDA3) at the position of the first reflected light. For Pound-Drever-Hall (PDH) frequency stabilization technology, the first reflected light of the optical cavity is the source of an error signal. Therefore, the combination of optical feedback and PDH frequency stabilization technology can be realized in the same CEAS system, which may improve the detection sensitivity of the system. To improve the efficient coupling of laser radiation into cavity resonances, the incident light spot radius is set to 0.556 mm by adjusting the zoom fiber collimator.