# L-Band Erbium Fiber Laser with Tunable and Narrow Sub-kHz Linewidth Output
## 1 Introduction  
To obtain the stable single-longitudinal-mode (SLM) output, fiber lasers have been designed with several constructions, such as the distributed feedback (DFB) [1], distributed Bragg reflector laser (DBR) [2], and typical linear and fiber ring cavities [3, 4]. As mentioned above, the fiber ring lasers are the most important, because the ring cavities possess the capability to evade spatial gain hole-burning in the linear fiber cavity by applying an intra-cavity isolator and allow us to insert more optical devices for specific operations [5]. Therefore, erbium-doped fiber (EDF) lasers exhibit output characteristics, such as narrow linewidth, high optical signal-to-noise ratio (OSNR), low phase noise, single-longitudinal-mode (SLM) and long coherence length [6, 7]. Due to the above-mentioned properties, the EDF lasers can also be used in many fields and applications, such as optical sensors, optical communications, bio-photonics, microwave (MW) photonics, optical spectroscopy, and instrumentations [8, 9, 10, 11, 12]. However, the homogeneous broadening of erbium, mode-hopping, and fiber cavity length could lead to multi-longitudinal-mode (MLM) oscillation which exists in fiber lasers [13]. Thus, to solve and eliminate the MLM noise of the EDF laser, different technologies have been proposed [14, 15, 16, 17, 18], such as using the unpumped EDF saturable absorber (SA), multiple fiber ring structure, utilizing narrowband fiber Bragg gratings (FBGs), inserting Rayleigh backscattering (RB) injection, and applying a Mach-Zehnder interferometer (MZI)-based filter to the fiber cavity. To select and tune the various wavelength outputs in the EDF-based laser configuration, the variable FBG [19], Fabry-Perot tunable filter (FP-TF) [20], and tunable bandpass filter (TBF) [18] have been added to the fiber ring resonator for tuning wavelength. Furthermore, the achievable wavelength selection bandwidth of fiber laser depends on the effective gain medium range of erbium ion. To achieve broadband wavelength-tuning scope, using the broadband erbium-doped fiber amplifier (EDFA) [21], two parallel EDFAs [22] and a hybrid optical amplifier [23] were applied inside the laser cavity as the gain medium. In 2015, [PERSON] et al. proposed a fiber ring laser architecture using an MZI design, which consisted of two parallel fiber rings that shared the unpumped doped saturable absorber (SA) and fiber Bragg grating (FBG) for SLM oscillation [14]. The MZI-based comb-based filter and unpumped SA-induced auto-tracking narrow bandwidth filter could achieve the linewidth output of 1.09 kHz. In 2013, [PERSON] et al. demonstrated an EDF laser by applying the cascaded Type I and Type II fiber ring secondary cavities to achieve SLM operation based on the Vernier effect to lead to the mode-filter operation in order to reduce the multiple longitudinal modes [8]. But the actual output linewidth of that EDF laser was not performed and discussed experimentally in their work. In 2017, [PERSON] et al. also presented a fiber compound ring laser, which was composed of a fiber optical tunable filter, a high-finesse ring filter, and a loop mirror filter, to provide a narrow filter performance and also obtain the average 3 dB linewidth of 8.8 kHz over 60 nm wavelength tuning range [15]. In 2007, to reach an output linewidth of 2.5 kHz, In 2007, [PERSON] et al. used a narrow optical filter, which was constructed with an apodized FBG and a high finesse FBG-based Fabry-Perot (FP) etalon, inside the fiber ring cavity to decrease the dense longitudinal mode noises [16]. In 2015, [PERSON] et al. applied Rayleigh backscattering (RB) in a tapered fiber with feedback injection in a ring cavity. The feedback RB injection ring laser cavity also needed a sub-ring architecture to suppress and narrow the output linewidth to sub-kHz [17]. Moreover, [PERSON] et al.