Propagation of the radially-limited vortical beam in a near zone. Part II. Results of simulation

Detailed analysis of diffraction of a vortical beam by a circular microaperture in a near zone with use of various algorithms of calculation is carried out: vectorial Rayleigh-Sommerfeld diffraction integral (RS), plane wave expansion (PWE), including Mansuripur's modification, and finite-difference time domain (FDTD) method realised in the R-Soft software product. Results of nonparaxial modelling for diffraction of a vortical beam by a circular microaperture show oscillating character of shadow area of a vortical beam: the size of a light vortex increases and decreases as the beam propagates, and it can be much less by size in comparison with predicted by paraxial theory. Such character is confirmed in a vector case also. In the work the algorithm of fast calculation of PWE has been modified on the basis of the approach offered by Mansuripur. At such modification the polarisation matrix has no singularity, but predicts appearance y-components at propagation even if initially the wave was completely x-polarised. The analysis of the expressions received for vortical beams shows, that axial values of total intensity will not be zero for vortical order |m|=