Fig. 1. (a) Simulated far-field intensity distribution and (b) photo of the beam far-field distribution at z = 10 m of the vortex beam.

Fig. 2. Setup of the micro-welding of Cu sheets with the ring-shaped vortex beam.

Fig. 3. Trapezoid laser pulse profile.

Fig. 4. (a) Top-view pictures of the Cu sheets welded with the Gaussian and vortex beams at different welded phases by changing the welding pulse width. All welding is performed in air. (b) The “good-welded” spots with the vortex beam.

Fig. 5. Typical 3D graphs of the surfaces for good-welded Cu sheets with (a) the Gaussian and (b) vortex beams.

Fig. 6. Welding pools of (a) the Gaussian and (b) vortex beams.

Fig. 7. Measured tensions of the welded Cu sheets at different (a) peak powers, (b) pulse widths, and (c) defocusing. The peak powers are 800 W and 1150 W for the Gaussian and vortex beams in (b) and (c), respectively. The pulse widths in (a) and (c) are 6.5 ms for the Gaussian and 12.5 ms for the vortex beams.