# Compact Single-Frequency MOPA Using a Silica Fiber Highly Doped with Yb\({}^{3+}\)
## 2 Materials and Methods  
The custom Yb-doped fiber tested as an amplifier (fiber I in Table 1) struck a compromise between the conflicting requirements mentioned above. It was highly doped with 0.25 at.% Yb (1.65 \(\times\) 10\({}^{+26}\) Yb/m\({}^{3}\)). It had a comparatively large NA (0.082), a 15-um core diameter, and it carried two modes at the signal (1064 nm). No bending loss was observed down to a bend diameter of 4 cm. Two commercial fibers (see Table 1) were tested for comparison. They were selected because their Yb concentrations, though significantly lower, rank among the highest for quality commercial fibers and because their cores are sufficiently small to provide a stable fundamental output mode. Their measured cladding absorption at 976 nm is ~3 times lower than fiber I. For all three fibers, the inner cladding diameter was either 125 um or 130 um. The fiber lengths in the amplifiers were selected to achieve a small-signal pump absorption of 20 dB to strike a balance between increasing the SBS threshold (shorter fiber) and increasing the pump absorption and output power (longer fiber). A high Yb concentration has the significant downside of increasing PD. PD manifests itself as an absorption loss at visible wavelengths with a tail extending to the 1-um region, where it causes harmful attenuation of the pump and signal. This loss increases with increasing Yb concentration and Yb inversion [24]. The most successful PD mitigation techniques include co-doping the core glass with P [21, 25] or Ce [21, 26]. These elements also raise the core index. This effect is corrected by adding index-lowering co-dopants such as F or B, or by using a pedestal index profile [26]. Al2O3 is also routinely used to increase the solubility of Yb2O3 in the core glass, hence limiting concentration quenching. Two common glass compositions are therefore Yb/Al/P [20, 21] and Yb/Al/Ce/F [27]. Our experimental investigations show that they both successfully mitigate PD while offering single-mode operation for Yb concentrations below ~0.15 at.%. For higher Yb levels, however, achieving single-mode operation is much more difficult due to the challenges associated with incorporating high fluorine doping levels. Adding more fluorine than in fiber I is possible, but it can result in a non-uniform mix of Yb, Al, and Ce concentrations (and refractive index) along the preform. To determine the optimum glass composition for our custom fiber, the suppression of PD was quantified by measuring the core loss induced by PD in three test fibers with different Ce/Yb ratios, numbered I, IV, and V (Table 2). They were custom aluminosilicate fibers with different concentrations of Ce but similar Yb concentration. A typical experimental setup [28] for accelerated PD evaluation was used. A short fiber (20-40 mm) was core-pumped with 450 mW of 976 nm light to ensure a nearly uniform Yb inversion of ~50%. Figure 1a plots the loss measured over time. After 20 h the PD loss was ~600 dB/m in the fiber with no Ce, ~200 dB/m in the fiber with a Ce/Yb ratio of 0.32, and ~33 dB/m for a ratio of 0.85. Thus, a prominent suppression of PD is observed even at a low Ce/Yb ratio of 0.32. However, it also shows that the Ce/Yb ratio should approach or exceed unity to achieve extremely low PD levels, in broad agreement with [21]. In light of this result, fiber I was selected for our amplifier work. Its Ce/Yb ratio of 0.32 was deemed sufficient because the inversion in the amplifier was much lower: 14.1% at maximum pump power. Its small-signal core absorption at 976-nm was ~1300 dB/m, which is ~1.3 times higher than in fiber II and ~3 times higher than in fiber III (see Table 1). Its cladding absorption was also higher due to its higher core-to-cladding areas ratio (as well as higher Yb concentration). Fiber IV was not selected, despite its higher resistance to photodarkening, because it had a