## 3 Experiments and Results
### Improvement of Working Stability by Electrical Feedback Control  
In this section, we set \(P=113\) mW, \(R_{1}=50/50\), \(R_{2}=10/90\), and \(I_{c}=0\), the working stabilities of MWEDFL are then tested in long and short terms, respectively. We find an obvious blue-shift occurs in the observed oscillation (@1560.46 nm) within a continuous 10-h (i.e., 600 min) operation. From Figure 7a, the total \(\lambda\)-shift is about \(\pm 0.1\) nm. And in Figure 7b the \(\lambda\)-shift in the short working term (50 min) is less than \(\pm 0.07\) nm. It means that the \(\lambda\)-shift of oscillations is small and stable in our designed MWEDFL. We define the change of \(\lambda\)-shift (denoted by \(\Delta\lambda\)) is  
\[\Delta\lambda=\frac{e_{\lambda}}{e_{\lambda 0}} \tag{5}\]  
where \(e_{\lambda 0}\) is the base line of \(\lambda\)-shift. We according to the results in Figure 7a,b set \(e_{\lambda 0}=0.08\) nm, and the corresponding fuzzy subset of \(\Delta\lambda\) is [MH (middle high), N (normal), ML (middle low)]. Its membership is shown as Figure 7c. Similarly, the changes of mean power in long and short working terms are presented in Figure 8a,b. The results show that the power fluctuation is over 1.0 dB but uniform within 10-h operation. Comparatively, there are some unexpected raises during the short-term testing and the total power shift also reaches \(\sim\)1.0 dB. This indicates the \(P\)-shift of oscillations should be much concerned in MWEDFLs. We define the change of \(P\)-shift (denoted by \(\Delta P\)) is  
\[\Delta P=\frac{e_{P}}{e_{P0}} \tag{6}\]  
Figure 6: The output spectrum of oscillations at \(P=113\) mW and \(R_{1}=50/50\), (**a**) coarse adjustment; (**b**) fine adjustment. Figure 7: The wavelength shift of oscillation at 1560.46 nm in the (**a**) long term (600 min); (**b**) short term (50 min) and (**c**) the membership of \(\lambda\)-shift. where \(e_{P0}\) is the base line of \(P\)-shift. Further we set \(e_{P0}\) = 0.6 dB according to the results in Figure 8a,b, and the corresponding fuzzy subset of \(\Delta P\) is {H (high), MH (middle high), N (normal), ML (middle low), L (low)}. Its membership is shown as Figure 8c. Furthermore, we respectively set the fuzzy subsets of \(\varepsilon_{\lambda}\) and \(\varepsilon_{P}\) are [PM, O, NM] and [PL, PM, O, NM, NL], and their corresponding memberships are shown in Figure 9. Consequently, the fuzzy rule bases for \(\lambda\)-shift and \(P\)-shift are given in Tables 1 and 2. We then set \(a_{1}\) = \(a_{2}\) = 6.9 \(\times\) 10\({}^{2}\) and \(I_{0}\) = 0.003 mA, so in the controller the value of \(I_{\lambda}\) is in the range of 0\(\rightarrow\)\(\pm\)2.07 mA, and \(I_{P}\) is in the range of 0\(\rightarrow\)\(\pm\)5.18 mA. Under the electrical feedback controlling, the working stabilities of MWEDFL are demonstrated in Figure 10. Obviously, the blue-shift of central wavelength is efficiently constrained. From Figure 10a,b, the long-term (10-h) and short-term (50-min) \begin{table}
\begin{tabular}{c c} \hline \(\mathbf{\Delta}\mathbf{\lambda}\) & \(\varepsilon_{\lambda}\) \\ \hline MH & NM \\ N & O \\ ML & PM \\ \hline \end{tabular}
\end{table} 
Table 1: Fuzzy Rule base of \(\lambda\)-shift. \begin{table}
\begin{tabular}{c c} \hline \(\mathbf{\Delta}\mathbf{P}\) & \(\varepsilon_{P}\) \\ \hline H & NL \\ MH & NM \\ N & O \\ ML & PM \\ L & PL \\ \hline \end{tabular}
\end{table} 
Table 2: Fuzzy Rule base of \(P\)-shift. Figure 8: The mean intensity fluctuation of oscillations in the (a) long term (600 min); (b) short term (50 min) and (c) the membership of \(P\)-shift. Figure 9: Factors of fuzzy control for (a) \(\lambda\)-shift and (b) \(P\)-shift. stabilities of wavelength shift are respectively \(\pm\)0.029 nm and \(\pm\)0.022 nm in our scheme. Furthermore, compared to the results in Figure 8, the power stability is dramatically improved by electrical controller. In Figure 10c,d, the power-shift is limited \(\pm\)0.182 dBm within 10-h period and the short-term shift of power reaches \(\pm\)0.141 dBm.