## 1 Introduction  
A single-frequency fiber laser at 1.55 \(\upmu\)m wavelength with narrow linewidth, low fiber transmission loss, and eye-safe properties has great application in many fields, such as LIDAR, coherence optical communication, high sensitivity fiber sensors, and so on [1, 2]. The erbium-ytterbium co-doped fiber (EYDF) amplifier is the main method for obtaining a high-power single-frequency laser because it can minimize the linewidth broadening. Compared with the erbium-doped fiber amplifier (EDFA), the amplifier with erbium-ytterbium co-doped fiber as a gain medium achieves high amplification efficiency by doping Yb-ions. In 2005, [PERSON] et al. demonstrated a high-power EYDF amplifier and obtained a 151 W single-frequency fiber laser with megahertz level linewidth [3]. We also obtained a 56.4 W high power 1.55 \(\upmu\)m fiber laser with a linewidth of 4.2 kHz through an EYDF amplifier in 2015 [4]. However, the Yb-band amplified spontaneous emission (Yb-ASE) in the EYDF with a wavelength range of 1000-1100 nm, not only affects the output signal-to-noise ratio (SNR) but also limits the amplification efficiency of the Er-band signal light. When the pump rate exceeds the cross-relaxation rate between Yb\({}^{3+}\) and Er\({}^{3+}\) ions, or in high power pump conditions, the upper-level population of Yb\({}^{3+}\) ions will accumulate and the Yb-ASE intensity will increase rapidly. This phenomenon, known as the pump bottleneck effect can reduce the conversion efficiency of the pump energy to Er-band signal and can become an important limitation in the power scaling, besides the stimulated Brillouin scattering (SBS). In 2007, the bottleneck effect was observed for the first time in an erbium-ytterbium co-doped fiber oscillator by [PERSON] et al. [5] and it has attracted the interest of researchers since then. Several effective Yb-ASE suppression methods have been reported in recent years. In 2010, [PERSON] et al. demonstrated that an auxiliary laser with a wavelength in the Yb-band injected in the EYDF and amplified with Er-band signal, together can avoid the accumulation of Yb-ions upper-level population [6]. In 2011 and 2012, [PERSON] et al. realized Yb-ASE suppression by reflecting part of backward Yb-ASE [7] or constructing a Yb-band ring resonator [8]. This auxiliary 1-\(\upmu\)m laser feedback method used in the EYDF amplifier was theoretically analyzed by [PERSON] et al. in 2011 [9]. They also experimentally obtained 40.4% slope efficiency by using FBG feedback partial backward Yb-ASE in 2015 [10]. Although the feedback of auxiliary 1-\(\upmu\)m signal can effectively reduce the intensity of Yb-ASE, this method needs additional components or laser source, which will increase the cost and insertion loss of the amplifier. Another effective way to improve the limitation of the bottleneck effect is by optimizing the pump wavelength. In 2016, [PERSON] et al. obtained the record highest output power (207 W) for a single-frequency 1560 nm fiber laser by using the 940-nm LD as the pump source [11]. The corresponding slope efficiency was 50.5%, which is also the highest efficiency for the EYDF amplifier up to now. The relationship between the pump wavelength and the intensity of Yb-ASE was simulated and analyzed by [PERSON] et al. in 2018, which provided a theoretical basis for optimizing the pump wavelength [12]. However, the commercial LD with specially optimized wavelength output is too expensive to be widely used. A simple structure, low-cost method is needed to suppress Yb-ASE effectively and improve the efficiency of the EYDF amplifier. In addition, the single-mode-multimode-single-mode (SMS) fiber structure has been widely researched because of its simple structure, low cost, and easy adjustment of output spectra [13; 14]. Due to the sensitivity of the environmental parameters, the SMS fiber structure is also used in sensing temperature [15], stress [16], vibration [17], the refractive index [18; 19], and so on.