Fig. 1. (a) Structure of an SA based on the nonlinear Kerr beam clean-up effect and (b) flowchart of our numerical model.

Fig. 2. Simulated energy proportion of the LP01 mode at the end of the short graded-index multimode fiber segment with different bending conditions. R, radius of curvature; L, curved length.

Fig. 3. Numerical results for the SA: (a) the evolution of modal energy proportion along the long GIMF segment when the laser wavelength is 1052 nm; (b) the transmittance of the SA versus input laser wavelength when the pulse energy is 50 nJ (red line) and 0.001 nJ (blue line); (c) the transmittance of the SA versus input laser intensity when the laser wavelength is 1052 nm.

Fig. 4. Experimental setup of the tunable mode-locked Yb-doped fiber laser based on NL-KBC effect. WDM, wavelength division multiplexer; GIMF, graded-index multimode fiber; Pol., polarization; D, diameter.

Fig. 5. Output power and conversion efficiency versus pump power. CW, continuous wave; CWML, CW mode-locking.

Fig. 6. Output characteristics of the laser when the pump power was 160 mW. (a) The single-pulse mode-locked pulse train. (b) The output RF spectrum with 1 Hz resolution bandwidth. Inset: the output RF spectrum with 100 Hz resolution bandwidth. (c) The output optical spectrum with a spectral resolution of 0.04 nm. Inset: the output optical spectrum with a spectral resolution of 0.1 nm. (d) The autocorrelation trace of dechirped output pulses with Gaussian fitting. Inset: the autocorrelation trace of output pulses with Gaussian fitting.

Fig. 7. Output spectra of the tunable mode-locked fiber laser with central wavelength ranging from 1040.7 nm to 1063.5 nm.