# L-Band Erbium-Doped Fiber Optimization and Transmission Investigation +
## 2 Fiber Optimization and Verification
### L-Band FM-EDFA Experimental Setup  
An experiment was conducted to characterize the designed L-band FM-EDFA. Due to the limitation of the mode converters, only 3 signal modes (\(\text{LP}_{01}\), \(\text{LP}_{11a}\), \(\text{LP}_{11b}\)) were tested. A schematic of the experiment is demonstrated in Figure 4. A tunable laser is used as the light source and connected with an optical switch to control the specific mode to be excited. After passing through a variable optical attenuator (VOA) for power adjustment  
Figure 3: **(a)** The iteration curves of \(G_{max}\) and \(DMG\). **(b)** The EDF’s performance in the L-band. and a polarization controller (PC) for polarization regulation, a mode-selective photonic lantern (MSPL) converts the fundamental mode to a specific mode with a low insertion loss of less than 1 dB. The signal power is \(-20\) dBm at the output of the MSPL. Two 1480 nm semiconductor lasers are the pump sources. The first few-mode 1480/L-band wavelength division multiplexer (WDM) combines the signal and the pump, and injects them into a 10 m long FM-EDF; the second WDM splits the signal and the pump and injects the backward pump into the FM-EDF. Finally, an optical spectrum analyzer (OSA, Yokogawa AQ 6370D, Tokyo, Japan) is used to measure the optical power. Before testing the modal gain, the ability to keep the quality of signal modes was verified: mode patterns at different positions were monitored by a charge-coupled device (CCD, Xenics, Bobcat 320 GigE). The specific test points are shown in Figure 5a, where point 1 and point 2 correspond to the common output port of the MSPL and the total output port of the designed FM-EDFA, respectively. Two typical wavelengths, 1590 nm and 1610 nm, were selected for this test. The mode patterns of these two wavelengths were captured to verify the ability to sustain the purity of the signal modes. To quantitatively measure the similarity between the input and output mode patterns, the cross-correlation factor (3) was employed, as defined in Equation (4) [20; 21]:  
\[C=\left|\frac{\iint\big{(}I_{in}-\overline{I_{in}}\big{)}\big{(}I_{out}- \overline{I_{out}}\big{)}dS}{\sqrt{\iint\big{(}I_{in}-\overline{I_{in}}\big{)} ^{2}dS\iint\big{(}I_{out}-\overline{I_{out}}\big{)}^{2}dS}}\right|, \tag{4}\]  
where \(C\) is the cross-correlation factor between input and output mode patterns, \(I_{in}\) is the mode intensity distribution of the input modes, \(\overline{I_{in}}\) is the average of the mode intensity distribution, \(I_{out}\) is the mode intensity distribution of the output mode, and \(\overline{I_{out}}\) is the average of the mode intensity distribution of the output mode. The value of \(C\) ranges from 0 to 1, with values closer to 1 indicating a higher degree of similarity between two mode patterns. The \(C\) is calculated at 1590 nm and 1610 nm and the results are shown in Figures 5b and 5c, respectively. This helps to assess the similarity between the input and output mode patterns at the specific wavelengths. As shown in Figure 5b,c, the cross-correlation factor C between the input and output mode patterns remains higher than 93.7%. This indicates that the designed FM-EDFA is capable of maintaining the mode purity of different mode groups. Figure 4: Schematic of the experimental setup of the designed L-Band FM-EDFA (VOA: variable optical attenuator, PC: polarization controller, MSPL: mode selective photonic lantern, FM-WDM: few-mode wavelength division multiplexer, OSA: optical spectrum analyzer). After verifying the ability to keep the purity of signal modes, the gain characteristics were measured, including modal gain, _DMG_, and optical spectra. The input powers of the three signal modes were set to \(-20\) dBm. The forward pump power was fixed at 400 mW, and the backward pump power was set to 450 mW. The transmission optical spectra of the three signal modes at the typical wavelength of 1600 nm are shown in Figure 6a-c. Additionally, the relationship between modal gain and backward pump power is shown in Figure 6d, with forward pump power held constant.