In this work we investigate the light patterns generated by paraxial radial and azimuthal polarization beams in type-II nonlinear crystal. We show that in paraxial case the second harmonic intensity pattern generated by the radial / azimuthal polarization beams can be expressed similarly to the Hermite-Gaussian HG 11 mode. In addition, numerical simulations were carried out taking into account diffraction, walk-off, and pump depletion. The numerical simulations have shown that even with pump depletion the resulting second harmonic beam consists of 4 maxima. Also, experimental results are presented, which confirm theoretical predictions. Interference patterns indicate phase shifts of π between neighbouring maxima.

We demonstrate collinear second harmonic generation performed with a beam with an embedded initial phase singularity of strength . We examine the law of topological charge conservation during this process. Despite the instability of the initial singularity, we observe a counterintuitive topological charge doubling. In the second harmonic, we observe an optical vortex of strength (topological charge) . The conservation of topological charge is confirmed by both numerical simulations and the experiment. We also provide a qualitative explanation of the process.

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In this paper we present the results of theoretical and experimental investigations of the optical vortex screw-dislocation position control based on optical vortex interference with the Gaussian beam. Optical vortices can be controlled by joining a Gaussian beam with a collinear optical vortex beam and changing the Gaussian beam intensity and phase. It is shown theoretically and experimentally that in this way it is possible to precisely change the optical vortex screw-dislocation position in plane transverse to propagation direction.