Dynamic characteristics for 2 μm-self-similar pulse thulium-doped fiber laser

A passive mode-locked thulium-doped fiber laser is a generator for 2 μm ultra-short laser pulses. In addition, mode-locked self-similar pulses also exhibit rich nonlinear dynamic characteristics in thulium-doped fiber lasers. Therefore, this article studies the dynamic characteristics of self-similar pulses for the 2 μm passive mode-locked thulium-doped fiber laser. The research results also indicate that as the gain coefficient increases, the peak power of self-similar pulses increases, pulse width widens, and the linearity of chirp increases.


Introduction
The fiber lasers provide an ideal platform for exploring the complex nonlinear dynamic behavior of mode-locked pulses.They not only have the advantages of compact structure, good stability, and high beam quality but also have the characteristics of easy dispersion adjustment and high nonlinear coefficient in fibers [1].
Due to the 1 μm-band and 1.5 μm-band passive mode-locked fiber lasers, the developments are relatively mature.Many studies on mode-locked pulse dynamics have been carried out in these bands, and many important breakthroughs have been made [2].In addition, mode-locked pulses also exhibit rich nonlinear dynamic processes in fiber amplifiers, making them an important method for studying optical phenomena such as high-energy pulse generation and self-similar pulses [3].
Self-similar pulses are typical mode-locked pulses formed in the near-zero positive dispersion region.This type of pulse avoids pulse splitting caused by nonlinear phase shift by generating linear chirp during transmission.Its time-domain characteristic is that the pulse contour is parabolic in shape and can selfevolve.Therefore, it can maintain the overall shape unchanged during transmission so that the pulse width and amplitude change proportionally [4].This pulse that evolves in a self-similar manner is also known as a similariton.The frequency spectrum is steep on both sides, and the top is convex, which can tolerate a higher nonlinear phase shift, resulting in a higher corresponding pulse energy.When selfsimilar pulses are amplified outside the cavity, they can maintain their linear chirp and parabolic pulse shape unchanged, making it easy to achieve pulse compression by eliminating chirp.They are widely used to achieve high-energy femtosecond pulses.
2 μm-band laser has a wide range of applications in scientific research and civilian applications, which has aroused great research interest.The 2 μm-band laser can achieve laser generation in other wavelengths, including wavelength conversion based on energy level transitions of rare earth ions and wavelength conversion based on nonlinear effects of the medium.It is widely used in laser surgery, optical communication, material processing, and so on.
In recent years, with thulium-doped fibers as gain media, the 2 μm-band laser pulse has also been deeply studied due to its wide application requirements.The related fiber device preparation technology and passive mode locking technology have become increasingly mature [5].This makes the passive mode-locked fiber laser and fiber amplifier in 2 μm-band an ideal platform for studying pulse dynamics.At present, not only are various mode-locked pulse forms implemented in this band, but also, due to the different optical properties of fiber materials in this band, some unique pulse nonlinear dynamics have become the focus of research.
Resonant cavity structure is the basic way to achieve high average power output for fiber lasers.Passive mode-locked thulium-doped fiber laser has not only the advantages of compact structure, economic practicality, and high stability but also flexible and controllable resonant cavity structure and parameters, making it an ideal platform for exploring mode-locked nonlinear dynamics.Therefore, a 2 μm-self-similar pulse thulium-doped fiber laser, as a new high-performance laser technology, is a frontier research field worth exploring.

Theoretical model
The mode-locking fundamental equation of the self-similar pulsed thulium-doped fiber laser is as follows: Where 2 is normal group-velocity-dispersion (GVD), and T is time scaled ; A stands for the normalizedpulse-amplitude (NPA), and g represents the fiber's gain. is the nonlinearity coefficient.

The generation and evolution of 2 μm-self-similar pulse when g= 0.6 m -1
The simulation result in Figure 1 shows that 2 μm-self-similar pulses are generated, which can maintain their respective waveforms unchanged during the propagation.As the pulse propagates, the pulse width and peak power gradually increase.
As shown in Figure 2, the 2 μm-self-similar pulse was obtained.The frequency of the 2 μm-band-self-similar pulse is shown in Figure 3. Figure 4 shows a good linear chirp achieved during the self-similar pulse evolution.

The generation and evolution of 2 μm-self-similar pulse when g= 0.7 m -1
Passively mode-locked 2 μm-band-self-similar pulse fiber laser has advantages over 1 μm-band and 1.5 μm-band for the distinct optical properties of 2 μm-band.The large gain bandwidth of thulium-doped fibers results in fundamental differences in their nonlinear dynamic characteristics.After changing the gain coefficient, the generation and evolution characteristics of 2 μm-self-similar pulses are shown as follows.
Comparing Figures 1-4 with Figures 5-8, we can observe that as the gain coefficient increases, the 2 μm-self-similar pulse width widens, the peak power increases, and the linearity of the chirp improves.

Conclusion
In summary, this article investigates 2 μm-band-self-similar pulses generated by a thulium-doped modelocked fiber laser, and the evolution process of parabolic pulses generated by the laser in the cavity was analyzed.Passive mode-locked thulium-doped fiber lasers provide a good platform for studying 2 μmband-self-similar dynamics.For passive mode-locked fiber lasers, their flexible resonant cavity parameters are conducive to achieving diverse mode-locking mechanisms.Studying the 2 μm-band-selfsimilar pulse dynamics characteristics is not only beneficial for revealing complex physical phenomena but also for better meeting practical needs by utilizing their pulse diversity.