## 3 Results  
### Optical Amplifier Characterization Results  
The measured peak power from the FLAT (data markers) can be seen in Figure 15. These values are adjusted for the added attenuation, but include the 31.7% losses from output fiber optics. The pump power shown in Figure 15 are pump powers at the entrance of the erbium doped fiber from the pump pickoff measurements. The seed peak power was \(\sim\)4.7 mW and the seed pulse width was \(\sim\)2.5 ns. When comparing the seed pickoff PIN with the amplifier output PIN at similar signal amplitudes, some measurements experienced a pulse width increase \(<\)10% while others had a negligible increase. In Figure 15, the 26 cm fiber appears to be approaching gain saturation at the 300 mW pump. The 55 cm fiber has two steps in the data, at around 75 mW and 225 mW, since this is where the attenuation was changed out during a fiber characterization and there was likely some variation in the attenuation from dust or particles. A similar attenuation step can be seen in the 86 cm and 106 cm fibers around 200 mW. Additionally, it can be seen in Figure 15 that the required threshold pump power to overcome signal absorption when the output peak power is greater than zero increases with increasing fiber length. The 55 cm fiber had the highest peak power at 300 mW pump power and the other three fibers had peak powers of approximately the same magnitude to each other, but less than the 55 cm fiber. If all fibers were identical except for length and if sufficiently high pump power was available at the erbium fiber entrance, the 86 cm and 106 cm fibers would have produced greater peak powers than the 55 cm fiber. The results from the dynamic simulation for a 26 cm, 55 cm, 86 cm, and 106 cm fiber (curves) can be seen in Figure 15. The pump power for each fiber was evaluated between 0 and 300 mW at the entrance of the erbium doped fiber. The seed laser pulse width and peak power used in each fiber simulation corresponded to the mean pulse width and peak power measured for each fiber during the FLAT characterization experiment. The seed peak powers were all selected to be \(\sim\)4.7 mW and the seed pulse widths were all selected to be \(\sim\)2.5 ns. The parameters that were iterated for each fiber separately to match the measured FLAT outputs can be found in Table 5. No value of \(C_{upcon}\) was specified for this fiber, but it was predicted that the \(C_{upcon}\) in all fibers would be close to one another. The reasoning for this assumption is that fibers of the same product model are likely to have the same manufacturing process, and thus should exhibit similar ion-to-ion interactions. The losses were a set of variables that could differ for all fibers, since the loss depends on how well light is coupled at the connectors. Variables that affect these connector losses include how well the fiber cores align, fiber geometric irregularities, and the finish quality of the connector. All of these variables can be different from fiber to fiber and can be difficult to characterize beforehand. Figure 15: The measured steady state peak power plotted with the simulated steady state peak power, using parameter values in Table 5, with four fiber lengths: 26 cm, 55 cm, 86 cm, and 106 cm. The data markers are the experimental measurements from the FLAT characterization experiment while the curves are from the simulation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fiber Len.** & \(C_{upcon}\) & **Extra Pump Loss** & **Extra Seed Loss** & **Extra Output Loss** \\ \hline
26 cm & \(2.44\times 10^{-23}\) & 1\% & 1\% & 1\% \\
55 cm & \(2.44\times 10^{-23}\) & 4\% & 4\% & 4\% \\
86 cm & \(4.36\times 10^{-23}\) & 27\% & 27\% & 27\% \\
106 cm & \(4.36\times 10^{-23}\) & 25\% & 25\% & 25\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation parameters used for all fibers in the FLAT simulation. The measured steady state peak power and the simulated steady state peak power match well for the two shorter fibers as seen in Figure 15, except for step in data for the 55 cm fiber.