## 3 Double-Clad Raman Gain Fiber  
For further improvements of the brightness, there is more potential in improving the beam quality than in improving the conversion efficiency. While it is well-known that SRS can improve the beam quality in GRIN-MM fibers [19], other multimode fiber structures such as double-clad fibers can be more effective in this regard and even produce single-mode output [20]. We therefore designed and fabricated a double-clad Raman gain fiber (DCRF) and evaluated it in a similar experimental setup. However, the loss of the DCRF is considerably higher than that of the commercial GRIN MM fiber, 7.5 dB/km at the pump wavelength and 6.9 dB/km at the Stokes wavelength, for light launched into the combined core and inner-cladding waveguide. It was therefore necessary to further improve the pump source. We replaced the 45 W diodes by ones that can provide 60 W of power from a 105 \(\upmu\)m core at an NA of 0.13. The new reflected diode source is wavelength-stabilized at 975.6 nm with \(\sim\)0.6 nm linewidth FWHM. The transmitted diode, which is not wavelength-stabilized, has a central emission wavelength in the range of 969.4-971.2 nm and a linewidth of 4 nm. The un-stabilized diode has higher transmission through the VBG than the previous stabilized one, and can also be taken to slightly higher power than the rated 60 W. When this diode is used on its own, the power through the VBG reaches 54 W. When the other diode is used on its own, the power reflected off the VBG reaches 35 W, which is comparable to the power with 45 W diode. We attribute the decrease in  
Figure 4: Experimental FR output spectrum at 20 W of laser output power from 1.5 km of GRIN fiber. reflection efficiency for the higher-power diode to its larger linewidth. In addition, the increased heating at higher power may perturb the VBG [21]. Figure 5 shows the transmitted and the reflected power from the VBG against the input power from the diodes. The maximum total combined pump power reaches nearly 85 W, compared to 70 W with the lower-power diodes. At the same time, the beam quality degraded from \(M^{2}\) = 22.2 to \(M^{2}\) = 23.2. Thus, the pump brightness improved by 11\(\%\) over that of the lower-power system, to 0.17 W\(\cdot\)sr\({}^{-1}\cdot\)um\({}^{-2}\). Our DCRF was manufactured in-house with the standard modified chemical-vapor deposition process. It has a pure-silica outer cladding surrounding a raised inner cladding and an embedded core, which are both doped with germanium in different concentrations to create the refractive index profile. The NA of the inner cladding is 0.3 with respect to the outer cladding, while the core-NA is 0.1 with respect to the inner cladding. The inner-cladding and core diameter are, respectively, 38 \(\upmu\)m and 14.6 \(\upmu\)m, with encircled areas of 1134 \(\upmu\)m\({}^{2}\) and 167 \(\upmu\)m\({}^{2}\) in the drawn fiber. The inner-cladding-to-core area ratio equals 6.8. This is below eight and therefore small enough to allow for efficient first-Stokes generation [22]. The fiber is protected by a low-index polymer coating, so also the outer cladding can guide light. The core supports two modes at the Stokes wavelength, \(LP_{01}\) and \(LP_{11}\). From the core refractive index difference of 0.036 to pure silica, we estimate the Raman gain coefficient to \(1.31\times 10^{-13}\) m/W for unpolarized light at 975 nm. Figure 6 shows the experimental configuration. In the same manner as for the multimode Raman gain fiber, the wavelength-combined pump beam was launched into the inner-cladding of the DCRF through a DM and a lens with a launch efficiency of \(\sim\)76\(\%\). A small fraction of the pump light, estimated to be 1.6\(\%\) was actually guided in the core, while we used high-index gel to strip out any light launched into the outer cladding. The Raman laser cavity comprised 0.65 km of the DCRF as the Raman gain medium and the same lens-coupled DM as before, high-reflection (HR) for pump and 1 st Stokes and with \(\sim\) 5\(\%\) reflectivity for the second Stokes.