There is a lots of different papers reporting about the propagation of the different types of an optical beams in a uniaxial crystals are known by that time. This beams are: Lager-Gaussian and Bessel- Gaussian beams. It is common for all this types of beams, that if propagation axis and crystal axis coincides, and accident beam had a circular polarization, are can get type spiral type degenerated umbilici, which corresponds to the charge 2 optical vortex in the orthogonal polarized beam component, generated by crystal [1] (Fig 1). This generation accurse due to total angular momentum conservation law symmetry axis of the crystal. One to the changing of the spin momentum which is associated with the beam polarization, this leads to the orbital momentum changes that associated with topological charge of formed orthogonal circular component. Double charged optical vortex could be easily perturbed by tilting beam axis with respect to the crystal axis. If the tilt angles are small (<0.1°) central umbilici splits on two lemons and the surrounding ring umbilici splits on two pairs of monster-star. The further increasing of the tilt angle leads to the topological charge of circular components becomes, equal, and additional orbital moment correspond to the beam mass center displacement.
Nowhere days, a Bessel beams are of a great interest because of their high importance in practical applications
in micromanipulations of micro particles and possibility to create a bottle-beams which employed in metal-cutting
machines.
Angular spectrum of a Bessel beam formed by a variety of a plane waves, belong to a hollow conical surface
with the angle 2β at the top of the cone. Take into account this fact, one can form a Bessel beam by means of the conical
lense-axicon. Generally speaking, we must note, that such a beam, formed by axicon changes it is shape along the
propagation axicon and become the beam corresponding to Bessel-Gaussian solution.
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