| Summary: | The single-pass second-harmonic generation (SHG) of a vortex beam under low fundamental wave depletion is systematically studied. Vortex modes at 1064 nm with integer topological charges from ±1 to ±9 and fractional ones at ±0.75 are generated by modulating the fundamental Gaussian beam with different spiral phase plates. The frequency doubling of these fundamental vortex modes is realized via single-pass SHG through the KTP. A detailed theoretical model is set up in the single-pass SHG of the vortex beams. Theoretical analysis indicates that the higher the order of the vortex beams, the lower the SHG efficiency, when the beam waists and fundamental power are given. The experimentally measured SHG output characteristics verify those obtained via theoretical analysis. Conservation of the orbital angular momentum during the SHG process is also verified, regardless of the fractional or integer vortex beams. SH LG<i><sub>0,2l</sub></i> vortex beams with high mode purity are obtained. The beam waists of fundamental/SH in KTP measured using a 4<i>f</i> system demonstrate that the Rayleigh ranges of the fundamental wave and SH wave are the same. The paper comprehensively presents some basic laws in the single-pass SHG of a vortex beam. In addition, it also indicates that SHG is an effective method to improve the mode purity of vortex beam.
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