## 2 Multimode Raman Gain Fiber  
To improve a fiber Raman laser one can improve the fiber, the cavity, or the pump source. We first investigated improvements possible with the same graded index multimode (GRIN-MM) fiber (OFS OM-4) we used before [15], in a similar cavity, but with a better pump source. For this, we spectrally combined two wavelength-stabilized pigtailed MM diode sources (IPG Photonics, PLD-70-975-WS). Each source can deliver 45 W of power from a 0.11 mm diameter core with an NA of 0.12. The diodes are spectrally offset from each other, at 974.6 nm and 975.1 nm, with linewidth of \(\sim\)0.5 nm (full width at half maximum, FWHM). The output beams were collimated and then combined into a single beam in an angled narrow-band volume Bragg grating (VBG, Optigrate model C38-48-C1) as shown in Figure 1. The VBG has an aperture of \(5\times 2\) mm, a thickness of 5 mm, and a FWHM bandwidth of 0.43 nm. The reflection efficiency for the 975.1 nm diode was \(\sim\)70\(\%\), and the transmission efficiency for the 974.6 nm diode was \(\sim\)80\(\%\). We reached 70 W of combined power (Figure 1b), without discernable degradation of the beam quality. The wavelength-combined pump light was launched into the multimode Raman gain fiber via a lens as shown in Figure 2. The launch efficiency was 60\(\%\). The Raman gain fiber has a germanosilica core with diameter of 62.5 \(\upmu\)m (area \(\sim\)3070 \(\upmu\)m\({}^{2}\)) and profile as shown in the inset of Figure 2. The numerical aperture is 0.275, which corresponds to a peak refractive-index difference to the pure-silica cladding of 0.026. From this, the Raman gain coefficient \(g_{R}\) can be estimated to \(1.19\times 10^{-13}\) m/W in the center of the core for unpolarised light at 975 nm [10,11]. The propagation loss was measured to 1.7 dB/km at the pump wavelength and 1.5 dB/km at the Stokes wavelength of 1019 nm. We used two lengths of  
Figure 1: (**a**) Experimental setup of the spectrally beam-combined diode pump source; (**b**) Reflected and transmitted pump power after VBG _vs._ input power of each diode. fiber, 3 km and 1.5 km. The effective lengths (\(L_{eff}\)), as determined by the actual length and the pump propagation loss, become 1.8 km and 1.1 km, respectively. In the far end of the fiber, a lens-coupled dichroic mirror (DM) with reflectivity of over 99\(\%\) for both of pump and Stokes, was used to launch escaping light back into the fiber with 80\(\%\) launch efficiency. The dichroic mirror has a reduced reflectivity of 5\(\%\) at the wavelength of the second Stokes around 1064 nm. This helps to prevent SRS to the 2 nd Stokes at 1064 nm, which can degrade the conversion efficiency [5]. The fiber had flat normal cleaves in both ends. Thus, the resulting 4\(\%\) reflectivity closed the laser cavity in the combined pump launch and out-coupling end of the fiber. There, another dichroic mirror separated the out-coupled beam from the pump path. The total roundtrip loss at the Stokes wavelength in the resulting linear laser cavity becomes 24.5 dB and 20.0 dB for the two different fiber lengths of 3 km and 1.5 km, respectively. Figure 3 shows the total laser output power measured from the 3 km and 1.5 km long GRIN-MM fibers, together with the results of theoretical calculations. Experimentally, the output power with the 3 km long fiber reached 15 W with a slope efficiency of 62\(\%\) and a threshold of 16 W. For the 1.5 km long fiber, the threshold increased to 20 W and the slope efficiency increased to 81\(\%\), while the output power reached as high as 19 W. This corresponds to a record optical-optical device efficiency of about 50\(\%\). We attribute the high power and efficiency to the low loss of the fiber, as well as the high pump brightness, which allows us to operate relatively high above threshold in fibers short enough to further reduce the impact of propagation loss. The thresholds correspond to single-pass gain slopes of 0.82 dB/W (3 km) and 0.50 dB/W (1.5 km). Figure 2: Experimental setup of the CW FRL with GRIN Raman gain fiber.