In this paper the transformation of Hermite-Gauss (HG) beams with embedded vortex phase by lens system is investigated theoretically and numerically. A particular attention is attended to the formation of vortex phase singularities in focal area. It is shown, that under appointed relations between HG mode indices and the number of embedded optical vortex, the vortex phase singularity in a focal plane centre may be disappeared. The modeling of the vortical HG beams propagation through a waveguide with a parabolic dependence of the refractive index is implemented on base of the fractional Fourier transformation (FrFT).
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