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

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Random fiber lasers are of tremendous interest to diverse applications for optical fiber sensing, speckle-free imaging. To date, random fiber lasers with fundamental mode oscillation have been well developed. However, controllable oscillating spatial mode in random fiber lasers have not been reported yet. Here, we propose and demonstrate a few-mode random fiber laser with a switchable oscillating spatial mode based on mode injection locking. An external signal light is injected to realize the locking of transverse mode in this random fiber laser and the direct oscillations of the fundamental mode, hybrid mode, and high order mode can be realized, respectively. This random fiber laser operates in the high-order LP11 mode stably with a threshold of as low as 88 mW. High efficiency and high purity cylindrical vector beams can be obtained by removing the degeneracy of the LP11 mode. This work may pave a path towards random fiber lasers with controllable spatial modes for specific applications in mode division multiplexing, imaging, and laser material processing.

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