## 3 Experimental Phenomenon and Theoretical Analysis
### Asymmetric Etalon Effect Phenomenon and Theoretical Analysis  
As shown in Figure 2, cavity-enhanced absorption spectra were detected at M1 and M2, respectively, and the measured results show that they have different characteristics. Specifically, the spectral data obtained after M1 has a ripple phenomenon except for some absorption lines during the laser's current tuning from 40 to 120 mA, while the data obtained after M2 does not. According to the conclusion of the previous analysis [20; 21], the spectral ripple effect is usually caused by the periodic change of the optical resonator loss with spectral scanning. In this case, the theoretical characteristics of the spectral data obtained after M1 and M2 should be the same, only the amplitude of the ripple is different. In fact, it can be seen that almost no ripple is found in the spectral data after M2. The ripple has significant interference with the absorption peak measurement, affecting the accuracy of spectral measurement and the minimum detectable absorption coefficient. In addition, this asymmetric etalon effect phenomenon significantly impacts the calibration of \"empty cavity loss\" by cavity ring-down (CRD) [22; 23]. Therefore, the mechanism of this phenomenon needs to be re-examined, and measures are taken to eliminate it. In this experiment, the optical resonator used is a U-shaped structure. In this case, the reflection of the surface behind M2 and M3 folded mirrors will not lead to the occurrence of the etalon effect due to the large incidence angle and large substrate thickness (\(\sim\)8 mm). However, for the end mirror M1, since the laser is incident vertically, the backside reflection of the cavity mirror substrate will introduce optical feedback, which forms an etalon with the coated reflection surface (with the surface light intensity reflectivity R\({}_{0}\) = 3.32% and  
Figure 2: The normalized OF-CEAS transmitted light signal detected at M1 (black) and M2 (red). The spectrum detected at M1 presents a periodic spectrum fluctuation including four absorption lines. The spectrum detected at M2 only has four absorption lines. \(\text{R}_{1}\approx 99.999\%\) for \(\lambda=1530\) nm). The light beam (A) at the mirror is split into multiple beams (shown in Figure 3a as A(n) and B(n)) by the two surfaces of M1 before coupling into the cavity. This reflecting process will produce an optical path difference between these beams. It can be inferred that the ripple effect of the M1 spectrum is caused by the multi-beam interference between the feedback light from the M1 substrate and the cavity resonance light. The transmission losses of M1 and M2 were measured using the cavity ring-down technique, and the results show that the transmission loss was about 10 ppm for M1 and 90 ppm for M2. There is a huge difference in the loss between the folded mirror and the end mirror. Therefore, this asymmetric etalon effect may be caused by the different losses of the two mirrors. To verify the conjecture, the transmission loss of the folding mirror M2 is changed, and the transmitted optical fields of M1 and M2 are simulated. The laser beam is Gaussian, considering the incident light A as follows in Equation (4):  
\[E_{i}(t)=A_{0}e^{-i(\omega t+kx)}(\omega=2\pi\
u) \tag{4}\]  
The spherical mirror has a divergent effect on the feedback light from the substrate, which causes the waist radius of the feedback light to increase. The coupling efficiency of the reflected light A(n) is calculated \(\phi=50\%\) according to mode coupling theory and Gaussian beam transform law [24; 25].