Q-switching (QS) and mode-locking (ML) are two fundamental operating regimes in pulsed lasers [1]. ML originates from the fixed phase relation (synchronization) of multiple longitudinal oscillating modes [2] while QS is a consequence of the modulation of the cavity Q-factor by reiteratively emptying and replenishing the stored cavity energy [3]. Tremendous effort has been made during the years to develop efficient saturable absorbers (SAs) to achieve QS [4–6] or ML [3,7–9] in lasers with high performance. Early theoretical analysis modeled the two regimes (i.e., QS and ML) in laser cavities through nonlinear polarization rotation (NPR) [10]. It is noteworthy that recent research that provides links between QS and ML experimentally investigated a novel buildup process of ML via QS by real-time characterization in a fiber laser, throwing light on some dynamics within the QS–ML transition [11]. All these investigations are based on single transverse-mode platforms.

In fact, there have been several investigations dealing with multimode issues, but mostly in the context of QS in solid lasers [12,13] and lately in a few-mode fiber cavity [14]. In addition, multimode fibers (MMFs) have been lately proven to be qualified SAs based on nonlinear multimode interference, facilitating QS [15] and ML [16–18] in fiber lasers. These lasers are essentially operated with a single transverse mode. As for multimode ML, however, a number of transverse modes along with the longitudinal modes nonlinearly interact in a more involved manner, wherein the spatial dimension becomes a crucial factor. Because of the inherent high-dimensional properties of multimode lasers, they provide ideal platforms to look into the complex nonlinear science and connect the nonlinear dynamics to various real-world physical phenomena. Remarkably, the recent successful demonstration of spatiotemporal ML (STML) in multimode fiber lasers [19] has opened up a new frontier of mode-locking and high-dimensional nonlinear dynamics. Then, a series of works related to STML were reported, including work on soliton molecules [20], self-similaritons [21], multiple pulses [22], wavelength-switchable pulses and hysteresis [23], dispersion-managed solitons [24], and vortices [25]. STML has also been realized in an all-fiber cavity using a multimode-fiber-based spectral filter [26] and achieved in cavities composed of MMF with a large modal dispersion [27]. In addition, near single-mode outputs were achieved by optimizing the spatiotemporal evolution in multimode lasers [27,28]. Despite current challenges to fully understand STML, a heuristic theoretical model has been put forward that is adaptive to more general cases, giving much insight into the mechanisms behind STML [29]. The boundaries of multimode fiber lasers are constantly being broadened over the years, showing abundant curiosities and promising perspectives. Nevertheless, there are few investigations on multimode QS in full-multimode fiber lasers, especially concerning the relation between multimode QS and STML.

In this paper, we report the experimental observation of steady multimode QS states and STML in a multimode fiber laser. Stable multimode QS operation is realized, with a typical result of a 1.88 μs pulse duration and a 70.14 kHz repetition rate. The output power is 215.8 mW, corresponding to the single pulse energy of 3.08 μJ. We find weak spatial filtering (or large spatial filter size) facilitates the formation of multimode QS, compared to the stronger spatial filtering strength to maintain STML in the same cavity. With an appropriate setup of spatial filtering and the SA (i.e., the NPR states), a reversible multimode QS–ML transition is achieved. The transition process can be tuned merely by changing the pump power, given fixed cavity settings. Furthermore, by carefully adjusting the waveplates and pump power, we realize a bistable state between multimode QS and STML. The spatial, spectral, and temporal properties of the output change as the laser operating regime switches in the QS–ML bistable state, without analogues in conventional single transverse-mode lasers. It is the first time, to the best of our knowledge, that the realization of the transition between multimode QS and STML as well as the QS–ML bistable state is reported.

To verify the features of the multimode QS, the pump power is decreased to 6.0 W (the threshold power for the QS regime corresponding to a certain NPR state and spatial filtering) and then raised to 8.0 W with a step of 0.1 W. The output power and corresponding repetition rate are, respectively, displayed in Figs. 2(c) and 2(d). It is clear that both the output power and the repetition rate rise when the pump power is increased from 6.0 W to 7.0 W. Correspondingly, the pulse width slightly declines from 1.92 μs to 1.81 μs. These results conform to the typical laws of QS regimes. Nevertheless, the repetition rate along with the output power appears to have reached the upper limit with an even higher pump power level [see the blue area in Figs. 2(c) and 2(d)], which is probably a consequence of the saturation of gain fiber. In addition, the QS state in the multimode fiber cavity tends to be unstable (a variation of the repetition rates) at some pump power levels, especially in the range above 7.0 W [See the repetition rate error bars in Fig. 2(d)].

To further verify the multimode properties of the QS states, we measure the output with spatial sampling and spectral filtering following the same method proposed in the literature [19,22,27]. Specifically, for the spatial sampling, the characterization of the output beam is conducted here by using a spatial sampler (e.g., a segment of fiber with a large numerical aperture) fixed on a three-axis stage to collect a small portion of the output light; for the spectral filtering, a set of bandpass filters with different pass bands are used to diminish certain modes with specific spectral components. In multimode fiber lasers, different spatial parts of the beam consist of different superposition of the transverse modes. On the other hand, different transverse modes generally have diverse spectra.

As mentioned above, to maintain stable QS states, it is necessary to obtain a high enough output power (or intracavity power) by optimizing the coupling between the light path in the multimode fibers and the free space, where weak spatial filtering confinement probably facilitates multimode QS generation. On the other hand, according to our experiment, if the light coupling is not as ideal as that of the previous setting already demonstrated to achieve QS (equivalent to a middle-size spatial filter), both STML and multimode QS can be achieved in the same cavity by adjusting the rotation angles of the waveplates. In other words, the STML and QS are supported simultaneously in the fiber laser cavity with a fixed pump power. Moreover, in certain cases, the transition between QS and STML can be achieved by merely altering the pump power. We note this kind of transition via pump power tuning is only supported with a specific cavity setup (i.e., SA, spatial filtering and light coupling), which possibly relies on the multimode gain response as well as the NPR-based SA effect.

Note that the underlying mechanisms of the transition as well as the bistability between multimode QS and STML are more involved than those in single transverse-mode lasers [10,11] since the participation of spatial (transverse) modes pushes the laser into a higher dimensional category [i.e., three-dimensional (3D)] which naturally complicates the transition dynamics. For example, the hysteresis of the QS–ML transition shows prominent distinction compared to that in single-mode platforms. In some cases (e.g., certain NPR states and cavity setup) in our experiment, the hysteresis is obvious. In other circumstances, however, hysteresis can rarely be observed (e.g., the bistable state shown in Fig. 5). Our demonstration of QS, multimode QS–ML transition, and the bistability has enriched the discovery of the curious properties and dynamics of 3D lasers. Spatiotemporal interactions (i.e., competition and compromise) among SA, the spatial filter, and the gain effect play significant roles in determining the operating regimes as well as the state evolution (i.e., transition, instabilities, and bistable states) of the multimode fiber laser. Spatial mode-resolved measurements and a real-time characterization must be carried out to fully understand the links between multimode QS and STML in future works.

In conclusion, we report the observation of multimode QS and STML in a multimode fiber laser. Multimode QS regimes are more likely to be supported with better cavity spatial coupling equivalent to a larger spatial filter size, according to our experiment. In addition, we have achieved a reversible QS–ML transition, which is strongly dependent on the pump power with a fixed cavity configuration. Furthermore, a critical bistability between the multimode QS and STML is realized under appropriate cavity spatial coupling and NPR states. The demonstration of multimode QS pulses generation and STML in multimode fiber cavities not only provides a promising and feasible way toward high-energy pulse engineering in fiber systems, but also sheds some light on the complex dynamics in 3D lasers concerning QS and ML buildup and evolution.