• Corpus ID: 230435639

Period-doubling bifurcation in spatiotemporal mode-locked lasers

@inproceedings{Xiao2021PerioddoublingBI,
  title={Period-doubling bifurcation in spatiotemporal mode-locked lasers},
  author={Xiaosheng Xiao and Yihang Ding and Shuzhen Fan and Changxi Yang and Xiaoguang Zhang},
  year={2021}
}

• X. Xiao, Yihang Ding, +2 authors Xiaoguang Zhang
• Published 1 January 2021
• Physics

Period-doubling bifurcation is a universal dynamic of nonlinear systems, which has been extensively investigated in laser systems with a single transverse mode. This study presents an experimental observation and theoretical investigation of the period-doubling bifurcation in spatiotemporal mode-locked (STML) multimode fiber lasers. In the period-doubling state, it is observed that the pulse train modulation varies with the transverse-mode, and the output beam profile fluctuates rapidly and periodically. The numerical simulations conducted in this study are in good agreement with the experimental observations. Furthermore, a simple iterative model is proposed by considering the mode-dependent saturable absorption effect, and the experimental results can be qualitatively interpreted by this model. Based on these results, spatiotemporal saturable absorption is believed to be the key factor for the unique spatiotemporal characteristic of period-doubling bifurcation in multimode lasers. This study contributes to the understanding of the complex spatiotemporal dynamics in STML multimode lasers and to the discovery of novel dynamics in high-dimensional nonlinear systems. Mode-locked lasers were typically operated in the form of a single transverse mode. Recently, spatiotemporal mode-locking was demonstrated in multimode fiber (MMF) lasers, which have subsequently attracted extensive attention. By using an MMF-based spectral filter, an all-fiber spatiotemporal mode-locked (STML) laser was realized. Additionally, an STML fiber laser with spatiotemporal self-similar evolution was demonstrated. Spatiotemporal mode-locking was achieved in a dispersion-managed MMF cavity, where pulse evolution was further achieved with Kerr-induced selfbeam cleaning to realize single-mode output. Recently, we demonstrated that spatiotemporal mode-locking could also be achieved in multimode cavities composed of MMFs with large modal dispersion, and a phenomenon of passive nonlinear auto-selection of single-mode mode-locking was observed. Automatic spatiotemporal mode-locking was achieved in a multimode fiber laser by using genetic wavefront shaping. A theoretical model, attractor dissection, was proposed to understand the mechanism of spatiotemporal mode-locking. Several forms of spatiotemporal mode-locking that have no analogues to the (1+1)dimensional system of single transverse-mode lasers have been identified. A model based on the (3+1)dimensional cubic-quintic complex Ginzburg–Landau equation was proposed, using which soliton breathers and vortices were predicted in STML MMF lasers. Mode-locked lasers provide an ideal platform to study the behavior of dissipative nonlinear wave dynamics. Within the multimode cavities, there are much more complex nonlinear behaviors compared with single transverse-mode lasers. STML lasers are expected to support abundant nonlinear spatiotemporal dynamics because MMF cavities can provide a test bed with both temporal and spatial characteristics. Soliton molecules, multiple-soliton, wavelength-switching and hysteresis have been observed in STML lasers. However, few STML states with spatiotemporal dynamics unique to multimode lasers were observed. Bifurcation is a universal dynamic of nonlinear systems, which has been observed in physics, biology, chemistry, and even economics. In laser systems, period-doubling bifurcation has been widely observed in semiconductor lasers, mode-locked solid-state lasers, mode-locked fiber lasers, etc. For the perioddoubling state of mode-locked lasers, the output pulse train is not uniform and alters periodically. Perioddoubling and pulsations in mode-locked lasers were theoretically investigated, and periodic pulsation was subsequently predicted in mode-locked fiber lasers. Then period-doubling bifurcation was experimentally observed in a mode-locked fiber lase. It was also observed that the soliton pulsation period can vary from a few to hundreds of roundtrips. Numerous investigations have been conducted on period-doubling bifurcation and pulsation in mode-locked fiber lasers, e.g., period-doubling of multiple solitons, periodical pulsations in Tm-doped fiber lasers, and optical frequency combs based on a period-doubling modelocked fiber laser. A simple iterative model has been proposed to characterize the generation of perioddoubling bifurcation. In the abovementioned investigations, only one transverse-mode exists in the mode-locked lasers. However, in the STML MMF cavities, there are multiple transverse modes and a new spatial degree of freedom. Hence, unique spatiotemporal characteristics are expected in multimode mode-locked lasers. Multiple-period pulsation has been briefly mentioned in the supplementary materials of Ref. [1]. However, period-doubling bifurcation in STML MMF lasers has not yet been reported. In this study, we report on the experimental observation and theoretical investigation of period-doubling bifurcation in STML MMF lasers. Our results indicate that in the period-doubling state, the nonlinear dynamics vary for different transverse modes. In the following, experimental observations are given first, then numerical simulations are introduced to validate the observed phenomena, finally a simple theoretical model is proposed to underline the physical insight of nonlinear dynamics in STML lasers. We built two types of STML fiber lasers, the experimental setups of which are described in Section 1 of the supplementary material. The 1 laser is composed of passive MMF and active quasi-single-mode fiber, and the gain competition among the transverse modes can be neglected. The cavity structure is similar to that used in our previous study and the first cavity mentioned in Ref. [1]. The core size (diameter of 10 μm) of the gain fiber is similar to those used in Refs. [2-5,13]. In this cavity, period-doubling bifurcation was experimentally observed and numerically validated, the details of which are explained in Sections 2 and 3 of the supplementary material. Although a variety of nonlinear dynamics (e.g., soliton molecule and period-doubling bifurcation here) have been observed in cavities with quasi-single-mode gain fibers, the cavity modes are restricted compared with full-multimode cavities. Therefore, a 2 fiber laser was built, composed of both multimode passive and active fibers, which is similar to that in our recent study. About six and dozens of spatial modes can be supported in the active and passive MMFs, respectively. A nonlinear polarization rotation (NPR) technique-based saturable absorber (SA) is used for mode locking and to compensate the modal dispersion of the MMFs. By adjusting the pump power and waveplates, spatiotemporal mode-locking with a uniform output can be easily achieved. However, period-doubling states can be achieved only in some sets of waveplates by further increasing the pump power. Typical uniform mode-locking is shown in Fig. 1(a), (c), and (e), which transitions to a period-doubling state by increasing the pump power, as shown in Fig. 1(b), (d), and (f). As shown in Fig. 1(a), the intensity of the output pulse train is uniform, and the pulse period is approximately 18 ns, which is in agreement with the fundamental repetition rate of 55.6 MHz. The corresponding radio frequency (RF) spectrum is illustrated in Fig. 1(c). There is no obvious sideband in this figure, implying that the output pulses are stable and uniform. The optical spectrum is shown in Fig. 1(e), and the multimode beam profile is displayed in the inset image. In contrast to the uniform mode-locking, the pulse train of the period-2 state, shown in Fig. 1(b), is not uniform; the pulse energy returns once every two roundtrips while maintaining the same interval. The RF spectrum is shown in Fig. 1(d), where there are two sidebands located at a frequency that is half of the cavity fundamental repetition frequency; this further validates the period-2 state. The optical spectrum and beam profile are shown in Fig. 1(f), which are slightly different from those in Fig. 1(e). When achieving the period-2 state, more period-doubling bifurcation is usually observed by further increasing the pump power. A typical state evolution is shown in Fig. 1(g) as pump power increases. In this figure, the STML state transitions from a uniform output to a period-2 state and then to a period-4 state. Fig. 1 Experimentally observed typical STML states of a,c,e uniform output and b,d,f period-doubling (period-2 state). a,b Pulse trains recorded by oscilloscope, c,d the corresponding RF spectra, and e,f the corresponding optical spectra (inset: beam profile). g A typical evolution of period-doubling bifurcation with an increase in pump power. In g, the y-axis represents the values of the single-pulse energies in the output pulse train, measured by a photodetector and oscilloscope. For uniform mode-locking, there is one marker; for pulsation states, there are several markers. To further investigate the spatiotemporal dynamics of the period-2 state, the output beam is spatially sampled and measured (setup shown in Fig. S1, similar to Ref. [12]). The extent of pulse fluctuation of the sampled pulse trains varies at different sampling positions; thus, the dynamics vary for different transverse modes. As an example, output pulse trains sampled at three different positions for the period-2 state of Fig. 1(b) are shown in Fig. 2(a). All sampled pulse trains still fluctuate with the period-2 state; however, they fluctuate differently, even out of phase. Figure 2(b) shows the extent of nonuniformity throughout the beam profile, and the corresponding beam profile is shown in Fig. 2(e), which is reconstructed as an intensity contour using 5 × 5 spatial samplings. As shown in Fig. 2(b), the intensity fluctuations of the sampled pulse trains vary extensively between 34%-188.5%. The experimental results show that the degree of fluctuation of the pulse train is different at different spatial positions (