## 3 Results and Discussion  
### DWCP and Pump Absorbed Rate  
Figure 3a shows that by changing the pump mode of the 1976 nm pump from a core pump to a clad pump, the 3.5 \(\upmu\)m laser was still available. However, the threshold was much higher, and the slope efficiency was lower, and the DWP scheme showed a saturation phenomenon as the power of \(P_{1976}\) increased. Changing the pump mode of \(P_{1976}\) from a core pump to a clad pump changed the mode overlap \(\Gamma_{1976}\). Therefore, the absorbed rate of \(P_{1976}\), \(\alpha_{1976}\) was different, given by:  
\[\alpha_{1976}=-\Gamma_{1976}(G_{VGSA}+G_{ESA2}+\alpha_{loss})\cdot P_{1976}, \tag{12}\]  
The difference of \(\Gamma_{1976}\) and \(\alpha_{1976}\) between these two schemes can explain the different optimization behaviors. The \(P_{1976}\) was absorbed much slower in the DWCP setup; thus, the stimulation threshold was higher, and the slope efficiency was lower. The saturation phenomenon called quenching was caused by the increasing ESA\({}_{2}\) process that depleted the Er\({}^{3+}\) ions in level \({}^{4}\)F\({}_{9/2}\)[15]. For a certain fiber, the quenching point is affected by the power of \(P_{976}\). Different powers of \(P_{976}\) yield different output power curves with similar tendency but different quenching points. Thus, in this paper, \(P_{976}\) was set as a typical power of 5 W, except in Figure 3. Since the power of \(P_{1976}\) was calculated up to 80 W, a matched \(P_{976}\) of 10 W was applied. The result showed that under the DWP scheme, quenching was more significant on a shorter fiber. For a longer fiber, quenching was delayed but the slop efficiency was reduced. Whereas under the DWCP scheme, considering the limited pump load capacity of the fluoride fiber, quenching was not a thing to be concerned about. This was because in this situation, quenching happened when \(P_{1976}\) went beyond 600 W. Figure 3a also shows that using a fiber with a proper length is a way to compensate for the low slope efficiency when using the DWCP scheme. The effect of fiber length was investigated in detail and is shown in the next section. Referring to the result in Figure 3a, the following simulations used 5-20 W of \(P_{1976}\) for the DWP scheme and 20-80 W for DWCP to make the output power compatible.  
Figure 3b shows that the DWCP scheme achieved a higher EO efficiency than the DWP scheme. EO efficiency was calculated as the output of the 3.5 \(\upmu\)m laser power divided by the total input electrical power of both pumps. The EO efficiency of the 2 \(\upmu\)m laser diode was from [12], and 15% was used in this simulation. Moreover, the EO efficiency of the 2 \(\upmu\)m fiber laser was measured from a homemade Tm\({}^{3+}\) fiber laser pumped by a 790 nm  
Figure 3: (**a**) Output power of a 3.5 \(\upmu\)m laser and (**b**) Electro-optical (EO) efficiency of a 3.5 \(\upmu\)m laser as a function of power of \(P_{1976}\). Simulated at \(P_{976}\) power of 10 W for the dual-wavelength pump (DWP) and dual-wavelength-clad-pumped (DWCP) schemes.  
commercial laser diode, which was about 2.1%. The 1976 nm laser diode had a higher EO efficiency but a lower absorption rate, and it turned out that a higher EO efficiency was achievable in the DWCP scheme.