## 3 Experimental Results
These phenomena prove that the resonance is coupled with a low-Q resonance. Note that \(g>0\), which satisfies \(g<\kappa_{\rm T}\) (\(\kappa_{\rm T}=1.31\times 10^{4}\)); this reveals that the two resonances are weakly coupled. This process proves the validity of the OD-PDH technique in analyzing weakly coupled resonances. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Fitting Object** & \(q_{1}\) & \(q_{2}\) & \(\Delta\lambda_{\rm d}\)/pm & \(g\)/MHz & **FCOD 3** & **RCOD 4** \\ \hline Figure 3a Res. 1 (\(g\
eq 0\)) & \(1.08\times 10^{6}\) & \(4.09\times 10^{4}\) & 173 & \(1.20\times 10^{4}\) & \(1.31\times 10^{4}\) & 0.997 & 0.997 \\ Figure 3a Res. (\(g=0\)) & \(9.22\times 10^{5}\) & \(6.10\times 10^{5}\) & 0.390 & 0 & 309 & 0.991 & 0.645 \\ Figure 3b IQ. 2 (\(g\
eq 0\)) & \(1.06\times 10^{6}\) & \(4.08\times 10^{4}\) & 173 & \(1.20\times 10^{4}\) & \(1.31\times 10^{4}\) & 0.998 & 0.994 \\ Figure 3b IQ. (\(g=0\)) & \(1.80\times 10^{6}\) & \(9.78\times 10^{5}\) & 0.259 & 0 & 260 & 0.999 & 0.893 \\ \hline \hline \end{tabular}  
* Res., Resonance. 2 IQ., IQ curve. 3 FCOD, Fitting coefficient of determination (Fitting R-Square). 4 RCOD, Replotted coefficient of determination (Replotted R-Square).  
\end{table} 
Table 2: Weakly coupled resonance fitting results. Figure 4a shows two resonances (blue scattered line) that are symmetrical and appear to be two independent resonances, and their IQ curves (black scattered line), when the pressure is 0.229 bar. We used a strongly coupled expression to fit both the IQ curve (red solid line) and the spectrum (yellow dashed line) (IQ COD, 0.985; spectrum COD, 0.996), and used the fitted parameters to reproduce the spectrum (red solid line) and IQ curve (yellow dashed line) (replotted IQ curve COD, 0.983; replotted transmitted spectrum COD, 0.933). The results are summarized in Table 3. The spectrum and IQ curve were accurately reproduced. Note that only one group of fitting parameters can be derived, with g \(>\kappa_{\rm T}\), revealing that the two resonances are strongly coupled. To check that the two resonances are coupled, we injected air into the MBR to tune the resonance. Figure 4b plots the successive change of resonances as the pressure increases from 0.229 to 0.522 bar. Repeating the above fitting process, we found that the two resonances become closer to each other when \(g\) decreases and \(g>\kappa_{\rm T}\). This implies that the two resonances are most likely strongly coupled. This process proves that the OD-PDH technique is valid for strongly coupled resonances. Figure 3: (**a**) Experimental (black scattered line) and fitted spectrum (red solid line, \(g=0\); yellow dashed line, \(g=1.20\times 10^{4}\) MHz). (**b**) Experimental spectrum (blue scattered line) and IQ curve (black scattered line), fitted spectrum and replotted IQ curves (red solid line, \(g=0\) MHz; yellow dashed line \(g=1.20\times 10^{4}\) MHz). (**c**) Experimental spectrum (blue scattered line) and IQ curve (black scattered line), fitted IQ curve and replotted resonances (red solid line \(g=0\) MHz; yellow dashed line \(g=1.20\times 10^{4}\) MHz). (**d**) Asymmetrical resonance shifts as the MBR internal pressure (0.215, 0.320, 0.416, and 0.519 bar) increases. Finally, we provide a discussion to explain which model should be used. Strong coupling will lead to mode splitting and generate two separate resonances. Thus, the asymmetrical single resonance can only be an overlapping or weak-coupling resonance. The weak-coupling model should be used. Two separate resonances may originate from two strong-coupling and overlapping resonances and will generate four peaks in the IQ curve. We can roughly determine the coupling status by the IQ curve. If the two center peaks are lower than the two side peaks in the IQ curve, the two resonances are either simply overlapping or weakly coupled. The weak-coupling model should be used. If the two center peaks are higher than the two side peaks in the IQ curve, the two resonances are strongly coupled.