Fig. 1. Experiment setup. BC, beam combiner; STIN YDF, step-index ytterbium-doped fiber (Nufern LMA-YDF-20/125-9M); GRIN MMF, graded-index multimode fiber (Corning, 50/125); filter, spectral filter; OC, optical coupler (10% output); PC, polarization controller (PC1, PC2); PD-ISO, polarization-dependent isolator; pigtail fiber, passive step-index fiber matched with YDF (Nufern LMA-GDF-20/125-M).

Fig. 2. (a) Average output power versus pump power. The red line is a linear fit to show laser efficiency. STML, spatiotemporal mode-locking. The laser is in STML operation in the marked range. Typical pulse train under (b) 5 μs/div and (c) 356 ns/div monitored by the oscilloscope at a pump power of 8.6 W.

Fig. 3. Various proofs of STML. (a) 2D and (b) 3D beam profiles before STML. (c) Spectrum corresponding to different sampling points (1, 2) before STML. (d) 2D and (e) 3D beam profiles during STML. (f) Spectrum, (g) pulse train, and (h) RF spectrum corresponding to different sampling points (1, 2) during STML.

Fig. 4. Various output parameters of STML fiber laser. (a) Autocorrelation trace. (b) RF spectrum with 10 Hz resolution bandwidth and 50 kHz span; the inset is the RF spectrum over a 1 GHz span and 51 Hz resolution. (c) Measured spectrum in linear scale before STML and during STML. (d) Measured spectrum in log scale during STML; the inset is a detailed image at a center wavelength of 1054.5 nm, with a resolution of 0.01 nm.

Fig. 5. Intracavity evolution of the walk-off among spatial modes. The walk-off is represented by the temporal center of gravity (tc) for all considered modes relative to the fundamental mode (mode 1) in each fiber. Regions in orange, blue, red, and green represent the MM gain fiber, MM passive GRIN fiber, spectral filter (as well as a virtual spatial filter) and SA, and passive MM fiber, respectively. STIN, step-index; YDF, Yb-doped fiber; GRIN MMF, graded-index multi-mode fiber; SF+SA, spectral filter and saturable absorber. All six modes in the STIN fibers and modes 1–6, 9, 10, 13–15, and 43–45 in the GRIN MMF are considered in the simulations. The colors for the modes are the same for all fibers, as shown in the legend. Note that the curves of modes 2 and 3, and modes 4 and 5, etc., overlap.

Fig. 6. Beam profile before and during STML by increasing the pump power. The dynamic evolution process is shown in Visualization 1.

Fig. 7. Comparison of group velocities of the modes of GRIN MMF and STIN MMF relative to the fundamental mode.

Fig. 8. Pulse sequence recorded by oscilloscope at QSML state with (a) 2 μs/div and (b) 200 ns/div.