We have considered a new type of singular beams called as optical quarks. They have fractional topological charges being equal to half an integer and they possess rather unique properties. There are four types of optical quarks, even and odd ones, which reveal the opposite signs of topological charges. The sums or differences of the even and odd quarks form standard vortex or non-vortex beams with the topological charges of integer order. All the quarks in the same beam annihilate and the beam vanishes. We conducted an analysis of all possible combinations of even and odd optical quarks with different charges. What provided an opportunity to explore what interactions correspond to their "sum" and "difference."
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.
We have experimentally analyzed the topological reactions occurred in the elliptic vortex-beam transmitting
orthogonally to the optical axis of the SiO2 crystal. We have revealed that the oscillations of the polarization state when
propagating the beam are accompanied by reconstruction of the polarization singularities at the beam cross-section that, in
turn, entails the reconstruction of the wavefront in each circularly polarized beam component. Both synchronic oscillations of
the spin angular momentum and the sign of the vortex topological charge are expressing in a field structure as birth and
annihilation of topological dipoles. Also periodical conversion of the vortex ellipticity along the crystal length z and huge
splash of spin angular momentum were analysed. The run of the dislocation reactions in the beam component results in
converting the sign of the topological charge in the centered optical vortex, the distance of the vortex conversion being about
0.05 of the wavelength.
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