## Materials and Methods
### Optical Amplifier Characterization
The simulation utilized functions built into the RP Fiber Power software to account for optical effects. This dynamic simulation is able to evaluate optical powers along the fiber for a small time step. By combining the evaluated optical powers at every time step, the amplification of an optical pulse can be evaluated. The energy model used is the two level approximation of the erbium ion energy levels. Additionally, homogeneous upconversion (HUC) and pair-induced quenching (PIQ) were also accounted for in this model. The parameters used for HUC are the number of ions are included in the upconversion ion interactions and the upconversion coefficient (\(C_{upcon}\)), which is related to impact that HUC has on the ion energy level populations. For PIQ, the parameters used are the number of ions per cluster and the fraction of the total ions in clusters. The PIQ effects were accounted for by defining separate populations for pairs and single ions and using the PIQ function included in the RP Fiber Power software. Amplified spontaneous emission (ASE) was also accounted for with this software over a spectrum of 1520 nm to 1580 nm. These parameters, except \(C_{upcon}\), can be found in Table 3.  
In this simulation, a 1531 nm seed pulse is propagated through a single clad, erbium doped fiber core of 7.6 \(\upmu\)m in diameter. The fiber was pumped in the core with a 976 nm laser in a forward pump configuration. Optical signals were assumed to be guided along the fiber core with a Gaussian intensity profile. The doping was assumed to be uniform and contained in the fiber core. A doping  
Figure 11: The setup used for characterizing the FLAT. The optics before the entrance and after the exit of the erbium doped fiber were kept the same except the free-space attenuation on the U-bench. The erbium doped fiber was swapped out after a series of measurements at different pump power were made. concentration of \(37\times 10^{24}\) ions/m\({}^{3}\) seemed to fit better than the specification (\(39\times 10^{24}\) ions/m\({}^{3}\)) for all four fiber lengths. This is acceptable to use since it falls within the 10% doping concentration uncertainty specified by the manufacturer [15]. The losses of the seed and the pump at the entrance of the erbium fiber were set to be 4%. The exit loss for the signal was set to be 35.7%, which is 4% from the connector plus 31.7% measured from the output optics. The exit loss of the pump laser used was 99.9%, which was from the provided isolator data sheet (30 dB) and verified with measurements. These parameters can be found in Table 3. It is important to note for Table 3 that the emission and absorption cross sections were intentionally excluded, since they were not found on public sources. The values used were for the pump and seed wavelengths and were selected from a list in the RP software, which acquired the cross section values from the manufacturer. The current EDFA design for MOCT is a single stage with a 4 W maximum pump in a counter propagating configuration. This EDFA design was simulated using the model developed for the FLAT, with modifications for the fiber length, pump power, and pump propagation direction. The pump laser is the only component in this EDFA that consumes electrical power and for a pump laser with an efficiency of 35%, the maximum power consumption is \(\sim\)11.5 W. This EDFA is anticipated to amplify 1 ns wide and 5 mW peak seed pulses to 1 kW of peak power at the EDFA output. The pump power can be adjusted to ensure the seed pulse is amplified with only enough margin to close the optical link and reduce power consumption associated with unnecessarily large amplifier gain. The erbium doped fiber is 1.6 m of Liekki ER80-8/125 (nLIGHT, Inc., Vancouver, WA, USA), which has a large single mode core for 1.5 um light which makes it easier to couple the pump light and can increase pumping efficiency compared to small cores. This fiber also has a high doping concentration which has high gain per length of fiber (80 dB/m) and enables shorter fiber lengths for a particular gain.