## 1 Introduction  
Tunable laser sources in the mid-infrared range are widely used in laser spectroscopy, atmospheric pollution monitoring, remote detection, and differential absorption lidar. In particular, continuous-wave (CW) single-frequency mid-infrared laser sources with broad wavelength tunability are more suitable for high-resolution spectral analysis [1; 2; 3; 4] and atom physics [5]. Different techniques have been applied to obtain a mid-infrared laser source. Quantum cascade lasers have been proved to be a method to generate mid-infrared radiation and [PERSON] et al. have done extensive work in this area [6; 7]. A solid-state laser based on metal-ion-doped crystals can directly generate mid-infrared radiation; for example, research on a Fe:ZnSe laser has been reported [8; 9]. An alternative method to reach the mid-infrared wavelength range is to utilize nonlinear frequency downconversion devices such as optical parametric oscillators (OPOs). OPOs with wide wavelength-tunability and a narrow linewidth have become a very important mid-infrared laser source. Compared with birefringent phase-matched (BPM) OPOs, quasi-phase-matched (QPM) OPOs can utilize the largest nonlinear optical tensor element of nonlinear crystals, and make the three interacting waves (pump \(\omega_{p}\), signal \(\omega_{s}\), and idler \(\omega_{i}\)) collinearly propagate in nonlinear crystals so that the distance of nonlinear interaction is largely enhanced. Many QPM nonlinear materials such as periodically poled LiTaO\({}_{3}\) (PPLT), periodically poled LiNbO\({}_{3}\) (PPLN), periodically poled KTiOPO\({}_{4}\) (PPKTP), periodically poled KTiOAsO\({}_{4}\) (PPRTA), periodically poled GaAs, and periodically poled GaP have been studied. Among these materials, PPLN is an excellent nonlinear crystal for QPM OPOs, having a relatively high nonlinear coefficient (\(d_{33}\) -27.2 pm/V) with a wide transparent range (0.35-5 \(\upmu\)m). Compared with PPLN, MgO-doped periodically poled lithium niobate (MgO:PPLN) has a much higher photorefractivedamage threshold. Therefore, MgO:PPLN is widely used as a QPM nonlinear crystal in mid-infrared OPOs [10; 11; 12; 13; 14; 15].  
To obtain a narrow linewidth idler output from an OPO, a narrow linewidth pump laser source is necessary in the OPO system. In addition, additional wavelength-selective elements are generally utilized to suppress the linewidth of the oscillated signal in the OPO cavity. [PERSON] et al. presented a narrow linewidth PPMgLN OPO, and the linewidth of the 2.98 \(\upmu\)m idler was within 0.30-0.63 nm by theoretical analysis [16]. [PERSON] et al., demonstrated a singly-resonant CW OPO pumped by an all-fiber pump source, with a 3.17 \(\upmu\)m idler linewidth of 1 MHz [17]. [PERSON] et al., demonstrated a singly-resonant CW OPO operating without mode hops for several hours due to the good thermal control of the MgO:PPLN crystal [18]. Reflecting volume Bragg gratings (VBGs) have been widely used in laser devices to obtain a narrow linewidth output. For example, [PERSON] et al., reported a singly-resonant CW OPO with optimum extraction efficiency, in which a single-longitudinal-mode signal output was obtained by employing a variable-reflectivity VBG as the output coupler of a ring cavity [19]. In addition, [PERSON] et al., devised self-seeding dual etalon-coupled cavities in the OPO system pumped by a single-longitudinal-mode pulsed Yb-fiber laser. The linewidth of the oscillated signal was suppressed and the linewidth of the idler was efficiently narrowed [20].  
In this paper, we report our experimental work on a CW single-frequency MgO:PPLN OPO pumped by a CW single-frequency Nd:YVO\({}_{4}\) laser at 1064 nm. We obtained a CW single-frequency 3.68 \(\upmu\)m idler laser with an output power higher than 1 W. Wavelength tuning can be achieved through thermal control of the nonlinear crystal and use of the different grating periods.