# Compact Single-Frequency MOPA Using a Silica Fiber Highly Doped with Yb\({}^{3+}\)
## 1 Introduction  
The development of high-power single-frequency Yb-doped laser sources has been stimulated by both scientific interest and industrial applications. High-power lasers with a narrow linewidth (sub-kHz to 100 kHz), very low relative intensity noise (RIN) [1], and high beam quality are required in applications such as high-precision resonant fiber sensors [2] and nonlinear optical conversion [3]. The required output powers are up to hundreds of watts in the mid-infrared regime and tens of watts in the visible and UV regimes, ideally in a compact package form. A technique that has been extensively studied to meet these requirements is the fiber master oscillator power amplifier (MOPA). It is composed of a seed laser followed by one or more amplification stages utilizing rare-earth-doped fibers. Power scaling in a single-frequency fiber MOPA is often limited by the onset of stimulated Brillouin scattering (SBS) in the gain fiber. SBS arises from the interaction of acoustic phonons with the propagating signal wave, which is converted into a frequency-shifted, backward-propagating wave [4]. Several effective techniques have been developed to suppress SBS. Some of these techniques rely on modifying the modal or spectral properties of the seed laser [5; 6; 7; 8]. In spite of their effectiveness, most of these techniques require additional components that increase size, cost, and complexity,and degrade reliability. Other techniques mitigate SBS by modifying the gain fiber. These modifications include utilizing a special gain fiber, for example with a large mode area (LMA) [9, 10], a high Yb concentration [11], or a taper [12]. SBS has also been pushed back by applying a temperature [13, 14] or strain gradient [15] to the gain fiber. Achieving output powers in excess of 100 W requires more than one mitigation technique [9, 16]. These techniques are particularly essential when amplifying a signal with a linewidth narrower than the SBS gain bandwidth (~23 MHz in silica [17]), in which case the SBS threshold is low. Of the various classes of high-power Yb-doped fiber MOPAs, this paper is concerned strictly with single-frequency amplifiers with an output of 50-100 W with emphasis on minimizing size, cost, and complexity, even at the cost of a somewhat reduced output power. To this end, we consider only single-stage MOPAs, which in general utilize the fewest number of components and have the smallest footprint, and MOPAs that implement no SBS-suppression technique, for the same reasons. The highest output power reported for this class of amplifiers is 115 W [18]. It was achieved by bidirectional pumping and applying a temperature gradient to suppress SBS. A similar power was reported using a chirally-coupled-core (3C) fiber [16], although a large coiling diameter (0.3 m) was required. Intrinsic temperature gradient induced by backward pumping was used to achieve outputs of 20.1 W [19] and 108 W [9]. These devices required long fibers (~9 m), although the MOPA in [9] had a small bend diameter of 10 cm in spite of using an LMA fiber. To meet the joint objectives of SBS suppression and compactness, this work explores the use of a conventional step-index fiber with a high Yb doping level. Optimizing the design of such a fiber requires careful selection of several parameters that have opposing effects on performance. First, for SBS suppression, the Yb concentration must be as high as possible to minimize the fiber length. Second, the fiber must be single-mode or near-single-mode to ensure a diffraction-limited output. Third, to reduce the system's footprint, the fiber must be wound in a tight coil while inducing minimal bending loss to the fundamental mode. This implies that LMA fibers are not preferred, since they typically (though not always [9]) require a large bend radius. It also implies that the core mode must not be too weakly guided. Finally, for SBS suppression, the fiber must carry as large a mode as possible while remaining near single-mode.