# L-Band Erbium-Doped Fiber Optimization and Transmission Investigation +
## 2 Fiber Optimization and Verification
### L-Band FM-EDFA Experimental Setup
The blue curves are the optical spectra of the input signal modes; the black curves are the optical spectra of the output signal modes without the pump laser; and the red curves are the optical spectra of the output signal modes with pump lasers injected. Under this pump configuration, the modal gains of the three signal modes are nearly identical: the modal gains of the LP\({}_{01}\), LP\({}_{11a}\), and LP\({}_{11b}\) modes are 22.10 dB, 21.56 dB, and 21.88 dB, respectively. The _DMG_ is 0.54 dB. Figure 5: (**a**) Schematic of the mode pattern’s captured points. The mode patterns at different positions (�⃝1 and ⃝2) and cross-correlation factors (C) at (**b**) 1590 nm and (**c**) 1610 nm. Figure 6: The spectra of three signal modes in different conditions (1600 nm): (**a**) \(\mathrm{LP_{01}}\), (**b**) \(\mathrm{LP_{11a}}\), (**c**) \(\mathrm{LP_{11b}}\). (**d**) Modal gain and _DMG_ with the backward pump power. As shown in Figure 6d, the backward pump power is incrementally increased from 50 mW to 450 mW in steps of 50 mW. As the backward pump power increases, the signal power is recorded, and the modal gain and the \(DMG\) are calculated accordingly. The gains of the three signal modes grow almost synchronously, demonstrating the effectiveness of the active fiber optimization. Moreover, when the backward pump power reaches 400 mW, the minimum modal gain is 20.70 dB, and the \(DMG\) is 0.36 dB. The performance of the FM-EDFA is also evaluated at 1605 nm and 1610 nm under the same experimental conditions, except for the signal wavelength. The results are illustrated in Figures 7a and 7b, respectively. Compared to 1600 nm (Figure 6d), the modal gains of the three signal modes are lower at these two wavelengths. When the backward pump power is set to 450 mW, the modal gains of \(\mathrm{LP_{01}}\), \(\mathrm{LP_{11a}}\), and \(\mathrm{LP_{11b}}\) are measured to be 20.76 dB, 20.75 dB, and 19.20 dB at the wavelength of 1605 nm, respectively. While at 1610 nm, the modal gains of \(\mathrm{LP_{01}}\), \(\mathrm{LP_{11a}}\), and \(\mathrm{LP_{11b}}\) are 17.8 dB, 18.82 dB, and 18.24 dB, with a \(DMG\) of 1.14 dB. The modal gain and \(DMG\) were also measured in the wavelength range of 1575 nm to 1600 nm, with an interval of 5 nm. Combining these results and those presented in Figures 6 and 7, the comprehensive findings are illustrated in Figure 8: in this wavelength range, the signal at lower wavelengths obtains a higher modal gain. However, the \(DMG\) tends to be relatively higher at these lower wavelengths. Specifically, the maximum modal gain reaches 22.22 dB, and the DMGs are below 2.28 dB. Meanwhile, the gain flatness factor is introduced to quantify the gain flatness performance in a wavelength range:  
\[G_{f}=\mathrm{max}(Gain_{\lambda,MN})-\mathrm{min}(Gain_{\lambda,MN}) \tag{5}\]  
In Equation (5), \(\lambda\) represents the signal wavelength, \(MN\) represents the signal mode, and \(G_{f}\) is the gain flatness factor. The gain flatness factor in the wavelength range of 1575 nm to 1610 nm is 4.54 dB. This result demonstrates the good performance of the  
Figure 8: Modal gain and DMG with wavelength (experiment). Figure 7: Modal gain and DMG with the backward pump power at **(a)** 1605 nm and **(b)** 1610 nm. L-Band FM-EDFA. Consequently, the quality of a DSP-free transmission system applied with the designed FM-EDFA is verified in the following section.