Generation of high-order solitons with order continuously adjustable in a fiber laser based on GIMF–SIMF–GIMF saturable absorber
Introduction
High-order solitons also called bound states of solitons have attracted great attention due to their potential applications in optical communication, high-resolution optics, all-optical data storage, high-modulation information transmission, etc. [1], [2], [3]. Especially, the high-order solitons can be used as data-carrying symbols in the field of high-speed optical communication [4], [5], [6]. The number of solitons in the high-order solitons determines the amount of information that may be carried. Therefore, the study of high-order solitons, which contains more solitons is of great significance for high-speed optical communication. High-order solitons are high-order solitons solution of the nonlinear Schrödinger equation (NLSE), can be obtained in passively mode-locked fiber lasers and formed by the interaction between solitons [7], [8], [9]. When the pump power is increased to a high level, multiple-soliton will be generated in the laser cavity due to the peak power clamping effect and the soliton energy quantization effect [9], then these solitons are bound together through interactions to form high-order solitons [10], [11], [12].
Various passively mode-locked techniques have been utilized to generate bound solitons, such as: nonlinear polarization rotation technology (NPR) [8], [13], [14], figure-eight fiber laser [15] and two-dimensional material SAs mode-locked technology [16], [17], [18], [19], [20], [21]. In 2002, N.H. Seong and Dug Y. Kim used a figure-eight fiber laser to output a fourth-order soliton [15]. In 2013, R. Gomenyuk and O.G. Okhotnikov achieved seven pulses bound state soliton in a fiber laser based on semiconductor saturable absorber mirrors (SESAMs) by adjusting the PC in laser cavity [22]. In 2008, Adil Haboucha et al. reported the bound states of 350 pulses in a fiber laser mode locked by NPR [23]. In 2016, Wang et al. observed a second-order soliton in a fiber laser mode-locked by nonlinear polarization evolution [13]. In 2017, Li et al. observed second-order soliton and third-order soliton in a fiber laser with a microfiber-based WS2 saturable absorber [10]. In 2109, R. LÜ et al. used a saturable absorber made of MoS2/fluorine mica to generate second-order soliton bound state with a soliton separation of 2.7 ps in a passively mode-locked fiber laser [21]. In recent years, the saturable absorber based on a combination of different optical fibers have become subject to the extensive study of fiber lasers due to their unique optical properties, such as, nonlinear multimode interference (NL-MMI), self-phase modulation, and cross-phase modulation. In 2013, the single mode fiber–graded index multimode fiber–single mode fiber (SMF–GIMF–SMF) structure was demonstrated theoretically it can be used as a SA in mode-locked lasers based on the NL-MMI by E. Nazemosadat and A. Mafi [24]. Recent reports have shown that the SAs based on the NL-MMI can used to generate solitons in fiber lasers. In 2017, Wang et al. designed a hybrid structure of step index multimode fiber–graded index multimode fiber (SIMF–GIMF) as a SA in an erbium-doped fiber laser to output fundamental soliton with duration of 446 fs [25]. In 2018, the same structure was used to generate dissipative soliton in ytterbium-doped fiber lasers [26]. In 2019, the hybrid structure of no-core fiber (NCF) and graded-index multimode fiber (GIMF) was designed as a SA to obtained the tightly bound soliton pairs with separation of 2.07 ps in a fiber laser [27]. Although the high-order solitons have been successfully generated via above techniques or SAs, there are few reports about the generation of high-order solitons with order continuously adjustable. Therefore, it is interesting to generate high-order solitons with order continuously adjustable in passively mode-locked fiber lasers.
In this paper, we fabricated a GIMF–SIMF–GIMF SA with a high damage threshold. In the experiment, the SA was inserted into an erbium-doped fiber laser cavity with a negative net dispersion. Not only fundamental soliton with duration of 540 fs can be obtained, but second-order to eleventh-order soliton can also be achieved by adjusting the pump power and PC. It is worth noting that both increasing pump power and adjusting PC can affect the order of the high-order solitons. We explain that the generation of high-order solitons with order continuously adjustable is due to the pulse shaping effect of GIMF–SIMF–GIMF SA and the pulse peak power clamping effect.
Section snippets
Experimental setup
The GIMF–SIMF–GIMF SA has been proven to be used in mode-locked fiber lasers according to previous report of our research group [28]. Fig. 1(a) shows the schematic diagram of the GIMF–SIMF–GIMF SA, it consists a piece of GIMF (Yangtze Optical Fiber, length 20 cm, core/cladding 62.5/), a piece of SIMF (Yangtze Optical Fiber, length , core/cladding 105/) and a piece of GIMF (Yangtze Optical Fiber, length 20 cm, core/cladding 50/). Fig. 1(b) shows the microscope image of
Fundamental soliton
A fundamental soliton was obtained by adjusting the PC when the pump power was increased to 110 mW. Fig. 3 shows the spectrum, soliton train, autocorrelation trace, and RF signal of the fundamental soliton. In Fig. 3(a), the Kelly sidebands in the spectrum indicate that the fiber laser output optical soliton. Kelly sidebands are caused by constructive interference between the solitons and dispersive waves, which is an inherent characteristic of soliton fiber lasers with net anomalous dispersion
Conclusions
In this work, we report on the generation of high-order solitons with order continuously adjustable in an erbium-doped fiber laser mode-locked by a GIMF–SIMF–GIMF SA. Not only fundamental soliton with a duration of 540 fs can be obtained, but 2nd-order to 11th-order soliton can also be achieved by adjusting the pump power and PC. The GIMF–SIMF–GIMF structure based on NL-MMI was fabricated and used as a SA to generate high-order solitons, it has advantages of high damage threshold, easy
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work was supported by the Science and Technology Planning Project of Shenzhen Municipality, China (JCYJ20180306171923592, JSGG20190819175801678).
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Yaping Gan and Qianchao Wu contributed equally to this work.