# A Multi-Layer Erbium-Doped Air-Hole-Assisted Few-Mode Fiber with Ultra-Low Differential Modal Gain
## 3 Results and Discussions
It is defined as the corresponding output power when the saturated gain of each mode drops by 3 dB. The relationship between the gains of the proposed AH-FM-EDFA and the signal input power is investigated and simulated in the case of triple-layer doping design, as shown in Figure 5. From the figure, it can be seen that when the signal input power varies from \(-40\) dBm to 5 dBm, the DMG is relatively low (\(<\)0.35 dB). The gain equalization characteristics perform  
Figure 2: Different doping profile. (**a**) uniform doping; (**b**) double-layer doping; (**c**) triple-layer doping. well and the saturated signal input power of different modes can be regarded as equal, about \(-17.7\) dBm. The saturated output power of the AH-FM-EDFA can reach 20 mW, which means the maximum output capability of the amplifier. Figure 4: Gains and DMG versus signal wavelength. Figure 3: Gain characteristics under (**a**) uniform-, (**b**) double-layer, and (**c**) triple-layer doping design. (**d**) DMG versus fiber length. Since the gain characteristics of the AH-FM-EDF are optimized under the length of 1 m and 3000 mW pump power, the gains and DMGs under different fiber length and pump power are further analyzed, as shown in Figure 6. The gain and DMG are illustrated in Figure 6a, with the length varying from 0.5 m to 3 m. As the fiber length is more than 0.9 m, signal gains are higher than 20 dB. In range of 1 m to 1.8 m for the fiber length, the DMG remains lower than 0.3 dB. Figure 6b illustrates the gains and DMG as the pump power varies. It can be seen that gains of different guided modes are higher than 20 dB and the pump power is higher than 3000 mW, and meanwhile the DMG is stabilized below 0.2 dB. Although the optimization of the doping profile is considered in the case of 3000 mW cladding pumping and 1 m length of fiber, the proposed AH-FM-EDF still performs well in gain equalization under different fiber length and pump power. Furthermore, as the inevitable imperfections always occur in practical manufacturing, the influences on the fabrication tolerance characteristics of the proposed AH-FM-EDF are further explored. However, due to the fiber fabrication, the RI and radius control have been relatively mature. Herein, the discussion about the fabrication tolerance is focused on the central air hole and the doping concentration deviation. The fabrication tolerance on the radius of the central air hole is illustrated in Figure 7. When the air hole radius is under \(\pm 5\%\) and \(\pm 10\%\) offset conditions, the DMG of the AH-FM-EDFA remains lower than 0.3 dB over the whole C-band and the minimum gain of the amplifier can reach 20 dB at 1550 nm signal wavelength. Figure 5: Gain saturation characteristic. Figure 6: Gains and DMG versus (**a**) fiber length (under 3000 mW pump power) and (**b**) pump power (under 1 m length of AH-FM-EDF). The doping concentration variation is analyzed with \(\pm\)5% and \(\pm\)10% offsets. The results are shown in Figure 8, and Figure 8a-c correspond to \(N_{1}\) to \(N_{3}\). From the figure, it can be seen that when the doping concentration offset occurs in \(N_{1}\) and \(N_{3}\), the maximum DMG of the amplifier is up to 0.8 dB (under the deviation of \(\pm\)10%). And when the doping concentration happens to \(N_{2}\), low DMG (<0.4 dB) can be realized. Within the \(\pm\)10% fabrication tolerance on doping concentrations, DMGs over the whole C-band can be controlled within 0.8 dB. Thus, even if the fabrication error occurs in the doping process, the gain equalization characteristics still perform well, which is beneficial to the actual manufacturing. For the active air-hole fiber, the production of the AH-EDF was realized by the modified chemical vapor deposition (MCVD) process [25], and the femtosecond laser can be used to form the void in the fiber core [24]. Considering the development of the layer-doped technology, we believe that the fabrication of the multi-layer doped AH-FM-EDF can be realized.