Second-harmonic generation of power-exponent-phase vortex beams

In this work, the second harmonic generation (SHG) of power-exponent-phase vortex beams (PVBs) was first introduced and demonstrated, numerically and experimentally. To begin with, based on the coupled wave equations, the SHG model of the PVBs in the nonlinear crystal was derived to reveal the intensity and phase evolutions. The intensity distribution of the SHG, with dark cores of 2|l|, can be observed, which is consistent with the number of phase singularities, and satisfies the conservation of orbital angular momentum. Then, the experimental setup was established to verify the correctness of the simulations by applying the 5%MgO: PPLN crystal. The experimental results indicate that the SHG of PVBs can be obtained successfully with conversion efficiency of SHG exceeding 20.8%, of which the intensity distribution, as well as the interference pattern with plane wave, agrees well with the numerical simulation. These results establish a foundation for the SHG of PVBs, and would facilitate their applications in the fields of nonlinear optics, information optics and so on.