Optical vortices and Airy’ spiral in chiral crystals

We consider both theoretically and experimentally propagation of a singular beam along a single chiral crystal and a stack of two such crystals with the oppo-site signs of their chirality coefficients. We develop a matrix approach for de-scribing behavior of the beam singularities. The beams with the eigen polariza-tion turn out to carry centered optical vortices with double topological charges. At the same time, a circularly polarized beam, when propagating, acquires an addi-tional unrequited phase having much to do with the geometrical Pancharatnam phase. The sign of the phase is defined by a direction of polarization circularity. To display experimentally the distribution of the geometrical phase we suggest employing two circularly polarized beams with opposite the circularities. The spiral image appearing behind the binary crystal system and the polarization fil-ter represents a set of spiral and ring edge dislocations of the wave front. They outline a profile of geometrical phase of the beam. Such the dislocation system is known in optical crystallography. It is nothing else than the four-fold Airy' spi-ral. We show also that the system of a chiral crystal with a purely anisotropic crystal, as well as a single chiral crystal combined with a circular polarization filter, are able to form a dark spiral line, too. However, such the line does not represent the edge dislocation and is shaped by means of a chain of optical vor-tices.