## 4 Discussion  
Despite the higher power achieved with the MM GRIN fiber, the radiance is still higher with the DCRF, and nearly ten times higher than that of the pump, thanks to the higher beam quality. This is a key attraction of DCRFs. On the other hand the comparatively high propagation loss of the DCRF used here limits the output power and efficiency. While higher pump power in the fiber (to allow for shorter fibers) as well as lower loss are possible long-term remedies for this, it is also interesting to see what is achievable with the present power-level and fiber. Figure 8 shows how the theoretically calculated output power depends on the length of the DCRF for several out-coupling and re-launch efficiencies. With 100\(\%\) re-launch efficiency; it is theoretically possible to reach over 62\(\%\) conversion efficiency with 1\(\%\) out-coupling as shown in Figure 8a. This improvement is possible thanks to a fiber sufficiently short (\(\sim\)2 m) to make pump propagation losses negligible. Although the Stokes power of almost \(\sim\)4 kW circulating in the cavity (present in each direction) may be unrealistic, similar efficiencies are possible with, e.g., 10\(\%\) out-coupling, 12 m of fiber, and \(\sim\)400 W of circulating Stokes power with 100\(\%\) re-launch efficiency as shown in Figure 8a. An output coupling of 40\(\%\), which is more typical for a fiber laser, still allows for 57\(\%\) conversion efficiency with 92 W of circulating Stokes power in 60 m of fiber as shown in Figure 8b. However, with the 96\(\%\) of out-coupling from a perpendicularly cleaved fiber facet, the conversion efficiency is reduced to 28\(\%\) with our parameters, even if there are no re-launch losses as shown in Figure 8b. This is due to increases in threshold and propagation losses as the optimum fiber length increases to nearly 400 m.  
Figure 7: (**a**) Experimental FRL output power with DCRF _vs._ pump power; (**b**) Experimental FRL output spectrum at 6 W maximum powers with DCRF. In reality, the re-launch losses may well be significant (as they were in our experiments). Figure 9 shows several curves indicating the output powers which are possible with different re-launch and out-coupling ratios with 65 W of launched pump power. Figure 9 also contains data calculated with the re-launch efficiencies of 64\(\%\) at the high reflectivity end and 58\(\%\) at the out-coupling end as suggested by our curve-fitting to the experimental data of the DCRF. The output power becomes 6 W for the 650 m of fiber we used. This improves to \(\sim\)12 W, at the optimum fiber length of \(\sim\)200 m. Reduced re-launch losses allow for much larger improvements, as exemplified with several curves in Figures 8 and 9. Although it is certainly possible to improve the re-launch efficiency relative to our experimental/fitted values, Figure 9 suggests that already a re-launch loss of 1.25 dB (\(\eta=0.75\)) in a single end is enough  
Figure 8: (**a**) Simulations of the output power _vs._ DCRF length at pump power of 65 W (launched) for out-coupling ratio (R1) of 0.9 and 0.99 and for 100\(\%\) re-launch efficiencies for pump as well as Stokes wave in both ends of the cavity; (**b**) Simulations of the output power _vs._ DCRF length at pump power of 65 W (launched) for various out-coupling ratio (R1) and 100\(\%\) re-launch efficiencies. Figure 9: Simulation of output power _vs._ DCRF length at pump power of 65 W (launched) for different reflectivities of the output coupler (R1) and re-launch efficiencies (\(\eta_{1}\) corresponds to out-coupling end and \(\eta_{2}\) corresponds to high reflectivity end ). to reduce the conversion efficiency to 21\(\%\) with 40\(\%\) out-coupling. However, this out-coupling is not optimized. Figure 10 is similar to Figures 8 and 9, but the out-coupling is optimized for each fiber length. The highest conversion efficiency becomes 62\(\%\), in the absence of re-launch loss for short fibers, for which the pump propagation losses become negligible.