## 1 Introduction  
An intense development of low-loss fiber components for operation in the 2 \(\upmu\)m wavelength region has yielded the rapid progress of mode-locked all-fiber lasers emitting in this spectral region. Broadband ultrafast fiber lasers delivering pico- and femtosecond pulses have attracted significant interest in the research community because of their wide range of applications including spectroscopy, medicine, material processing, remote sensing, optical communications, nonlinear conversion, and supercontinuum generation [1]. Owing to the wide and smooth emission spectrum of Tm\({}^{3+}\) ions in silica, mode-locked Tm-doped fiber lasers (TDFLs) are very attractive and one of the most commonly used choices for the generation of ultrashort pulses at a wavelength of 2 \(\upmu\)m. However, the generation of ultrafast femtosecond optical pulses requires dispersion management of the laser cavity because most single-mode silica fibers and fiber components exhibit anomalous dispersion in the 2 \(\upmu\)m spectral region. When the total net dispersion is close to zero, a dispersion-managed soliton (i.e., stretched-pulse) with a large spectral bandwidth and short pulse duration after compression can be generated [2; 3; 4; 5; 6]. This mode-locking regime enables a shorter femtosecond pulse generation compared with soliton mode-locking. The two shortest stretched-pulses with durations of 119 fs and 173 fs were generated in non-fully fiberized TDFLs mode-locked by nonlinear polarization rotation (NPR) [4; 5]. However, ultrashort pulses with durations of \(\sim\)200 fs and 253 fs emitted from all-fiber laser setups have also been reported [2; 6]. Near-zero cavity net dispersion, under strong pumping multiple dispersion-managed solitons, can be generated in a passively mode-locked fiber laser. When two or more fundamental solitons circle in the laser cavity, they propagate with the same velocity and can form a bound state. Bound states of solitons have been firstly studied numerically as high-order soliton solutions of the nonlinear Schrodinger equation [7, 8]. The first experimental demonstration of its generation in a fiber laser was reported in 2001 in an Er-doped ring fiber laser [9]. Then, bound states of solitons were reported and intensively investigated in fiber lasers with different total net dispersion--the large normal and anomalous cavity dispersion as well as in a dispersion-managed fiber laser with near-zero cavity net dispersion [10, 11, 12, 13, 14]. In 2019, bound solitons with tunable spectral bandwidth and pulse width as well as soliton separation were demonstrated in an Er-doped fiber laser with normal net dispersion [13]. Bound states have been also described in the 2 \(\upmu\)m wavelength region in TDFLs with slightly anomalous net dispersion and mode-locked by NPR [14]. These specific types of ultrashort pulses with fixed separations might be applied in optical communication to enlarge the data-carrying capacity of fiber link [15, 16]. However, reports on bounded solitons in the 2 \(\upmu\)m wavelength region are still sparse. Another mode-locking regime, which enables the generation of an optical pulse trace with a relatively high average output power and high pulse packet energy, is noise-like pulse (NLP) generation. This mode-locking operation commonly occurs in different types of passively mode-locked fiber lasers independently of laser cavity dispersion. NLP generation, characterized by a smooth and broad optical spectrum [17, 18, 19, 20, 21, 22], is a packet of multiple ultrashort pulses with randomly varying intensities and durations inside a longer envelope [22]. Owing to their relatively high output power, they are capable sources for various applications that do not require highly coherent pulses, such as supercontinuum generation, material processing, or low-coherence interferometry and sensing [23, 24, 25, 26]. Furthermore, NLPs can also be used in data storage, optical communications, or temperature profile measurements [27, 28, 29].