Abstract：We firstly report mode-locked square-wave pulse in Yb-doped fiber laser based on graded index multimode fiber of reverse suturable absorption. By adjusting the pump power, the width of the square-wave can be tuned range from 350 ps to 52.6 ns with 3dB bandwidth spectrum of 0.73 nm. The supermode suppression ratio exceeds ~ 65 dB, which indicates excellent mode-locked operation state, and we also study the characteristic of pulse by the chirp measurement system. The mode-locked square-wave pulse fiber laser can sever as high power light source for industrial applications. IntroductionAll-fiber-format mode-locked laser has been widely applied among biomedicine, scientific research, and industry due to its compact structure, excellent beam quality and efficient pumping [1]. It is significant to increase the energy of single pulse for the practical application of laser. The traditional soliton pulse energy is limited by the theory of soliton area and is generally limited to the level of hundreds pJ [2]. Diverse approaches have been proposed such as stretched soliton and parabolic pulse, however, these solitons can only output at most a few tens of mJ [3][4][5]. Akhmediev theoretically investigated dissipative soliton resonance (DSR) pulse forming mechanics based on cubic-quintic Ginzburg-Landau equation (CGLE) [6]. The characteristic of the pulse is that the energy pulse could increase indefinitely as pump power increases while simultaneously the amplitude remains constant, which is represented in the time domain as flat-top or square-wave pulse. This idea attracted a lot of researches, which led to a large number of published research results and improved the pulse energy to the level of μJ [7-9].To date now, mode-locked square-wave pulse are generally generated based on the nonlinear amplifying loop mirror (NALM) technique [10][11][12], nonlinear polarization rotation (NPR) mechanism [13]. It is rarely reported that new materials are used as saturable absorbers to generate square-wave pulses due to the damage threshold of these materials is generally low, they cannot withstand large energy pulses. Recently, the nonlinear switching properties or saturable absorber (SA) based on nonlinear multimode interference in graded-index multimode fiber (GIMF) has been widely investigated, which is superiority of low-cost, simple structure, and especially the ability in supporting extremely high damage threshold in high power double cladding fiber laser. It has already used as a saturable absorber in ultrashort fiber laser [14][15][16], however, there is no mode-locked square-wave pulse by adopting GIMF reported so far.In this paper, we firstly experimentally demonstrate the reverse saturable absorption effect in GIMF, which adopt our group proposed a new design of saturable absorber based on offset-spliced GIMF, and use it to output mode-locked square-wave pulse in Yb-doped fiber laser. In our fiber

Spatiotemporal mode‐locking (STML) in fiber lasers are of interest in applications such as optical communications, nonlinear imaging, and precision machining. To date, STML fiber lasers in the near‐infrared region have been well demonstrated, yet operation at visible wavelengths is still challenging. Here, a STML picosecond fiber laser at 635 nm with the implementation of Pr3+$^{3+}$/Yb3+$^{3+}$ co‐doped few‐mode fiber and nonlinear polarization rotation technology is reported. By solving the modified generalized multimode nonlinear Schrödinger equation, the 635 nm STML formation is theoretically predicted and analyzed. The stable 635 nm STML with a 9 ps pulse duration, which is two orders of magnitude narrower than previously reported, is realized experimentally. Moreover, spatiotemporal profiles are illustrated by investigating the locking of transverse and longitudinal modes simultaneously. By further establishing visible ultrafast fiber amplifier, the 635 nm average power is boosted up to 440 mW, corresponding to a maximum pulse energy and peak power of 4 nJ and 280 W, respectively. The experimental results are in good agreement with the numerical simulations. This work helps to understand nonlinear dynamics in STML fiber laser and directly generate large‐energy ultrashort pulses in visible  region.

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