# Gain Equalization for Few-Mode Erbium-Doped Fiber Amplifiers via Strong Mode Coupling
## 3 Results and Discussion  
To study the role of mode mixing in reducing the DMG in FM-EDFAs, we compared the DMG of a Type-A 6-mode EDFA with and without strong MC. Figure 3 shows MG as a function of EDF length at a pump power of 1 W, which is much higher than the signal power of 0.1 mW mentioned in Section 2. In an uncoupled case (Figure 3a), MG gradually increases until saturation point at \(\sim\)12 m and the overall DMG of the amplifier is reached at \(\sim\)9.3 dB. In a strong mode coupling regime (Figure 3b-d), however, a 6-mode EDFA can obtain a much lower DMG by increasing the degree of the MC, equivalent to increasing the CS or NCP. For example, as shown in Figure 3d, the DMG is reduced to 3.4 dB when NCP and CS are 600 and \(-\)10 dB/pt, respectively, which is 5.9 dB lower than that in Figure 3a. Then, we focused on the effect of NCP and CS on DMG reduction in strongly coupled FM-EDFAs. Figure 4 shows the calculated DMD results of both Type-A and Type-B 6-mode EDFAs. NCP and CS are in the ranges 10 to 600 and \(-\)25 to \(-\)1 dB/pt, respectively. It should be noted that there are little variations in the calculated DMG values at fixed NCP and CS, resulting from the randomness of the coupling matrix and the location of each point. We calculated the DMG at each NCP and CS an average of 100 times. In the uncoupled case, the DMGs of Type-A and Type-B fiber amplifiers were 9.3 dB and 2.4 dB, respectively, but it was greatly improved by strong mode mixing. In particular, for the Type-A EDFA, an 8.2 dB DMG reduction (i.e., from 9.3 to 1.1 dB) was achieved via strong mode mixing, and the DMG of Type-B EDFA was reduced to 0.5 dB with the aid of optimized Er-dopant distribution. Therefore, we can say that the proposed approach is very powerful for high DMG amplifiers, but it is also very useful to further reduce it in moderate-DMG amplifiers. Figure 3: MG as a function of EDF length in (**a**) uncoupled or strongly coupled 6-mode EDFAs; (**b**) NCP = 300, CS = \(-\)15 dB/pt; (**c**) NCP = 300, CS = \(-\)10 dB/pt; (**d**) NCP = 600, CS = \(-\)10 dB/pt. As mentioned before, NCP and CS are the key factors in reducing DMG. Considering the randomness of the coupling matrix and the location of each point, we then evaluated the DMG fluctuation of strongly coupled FM-EDFAs after 100 repeated calculations. We noticed that the DMGs of the two types of FM-EDFAs follow a similar trend as a function of NCP and CS (see Figure 4) and we chose a Type-A fiber amplifier (i.e., uniform doping), which is the most common and easiest to manufacture, for the following analysis. Figure 5 shows DMG and its corresponding standard deviation as a function of NCP and CS. As shown in Figure 5a, the DMG gradually decreases with CS and we can achieve a 7.8 dB reduction from 9.3 \(\pm\) 0.3 to 1.5 \(\pm\) 0.3 dB when NCP equals 300, as well as an 8.2 dB reduction when NCP equals 600. The DMG also decreases with NCP in Figure 5b from 8.6 \(\pm\) 0.3 to 4.4 \(\pm\) 0.7 dB when CS = \(-\)15 dB/pt and from 8.4 \(\pm\) 0.5 to 2.7 \(\pm\) 0.4 dB when CS = \(-\)10 dB/pt. It is worth noting that the standard deviation of DMG increased at the beginning due to the small number of NCP but decreased with NCP. The average MGs and DMGs of (un)coupled FM-EDFAs were studied at different pump powers. As shown in Figure 6a, the average MGs in both cases are almost the same and the DMGs remained unchanged for pump power in the range of 200-1000 mW. Apart from low DMG, it was also important to obtain wideband operation and low noise figures (NF) for FM-EDFAs. Figure 6b shows the average MGs and DMGs over the full C-band. In both cases, the average MG spectra of the amplifiers was flat over the whole C-band and the wavelength dependence of the DMGs was also negligible. Thus, the gain bandwidth and flatness of the amplifier was not sacrificed via strong mode mixing in FM-EDFAs. Figure 4: DMG of (**a**) Type-A and (**b**) Type-B 6-mode EDFAs as a function of NCP and CS.