Engineering of the space-variant linear polarization of vortex-beams in biaxially induced crystals.

We considered the propagation of Bessel beams through the biaxially induced birefringent crystal implemented by the mechanical torsion of the uniaxial crystal around its optical axis. Analyzing the solutions to the wave equation in the form of eigenmodes, we found that the system enables us to convert the beams with a uniform distribution of the linear polarization at the beam cross section into radially, azimuthally, and spirally polarized beams. Moreover, we revealed that the above system permits us to convert the beams with the space-variant linear polarization in accordance with the rule -s⇄s+1, where s is the topological index of the centered polarization singularity.

Rotational spin Hall effect in a uniaxial crystal.

We have considered the propagation process of the phase-matched array of singular beams through a uniaxial crystal. We have revealed that local beams in the array are rotated when propagating. However the right and left rotations are unequal. There are at least two processes responsible for the array rotation: the interference of local beams and the spatial depolarization. The interference takes place in the vortex birth and annihilation events forming the symmetrical part of the rotation. The depolarization process contributes to the asymmetry of the rotation that is called the rotational spin Hall effect. It can be brought to light due to the difference between the envelopes of the dependences of the angular displacement on the inclination angle of the local beams or the crystal length reaching the value of some angular degree. The direction of the additional array rotation is exclusively defined by the handedness of the circular polarization in the initial beam array.

Topological activity in Bragg elliptical twisted fibers.

We have theoretically shown that Bragg twisted elliptical fibers manifest, in certain spectral regions, the property of topological activity--the ability to change in the reflected field the topological charge of incoming optical vortices and fundamental modes by two units. This property could be used for narrowband generation of optical vortices from Gaussian beams and for changing the topological charge of incoming optical vortices.

Spatially engineered polarization states and optical vortices in uniaxial crystals.

We describe how the propagation of light through uniaxial crystals can be used as a versatile tool towards the spatial engineering of polarization and phase, thereby providing an all-optical technique for vectorial and scalar singular beam shaping in optics. Besides the prominent role played by the linear birefringence, the influence of circular birefringence (the optical activity) is discussed as well and both the monochromatic and polychromatic singular beam shaping strategies are addressed. Under cylindrically symmetric light-matter interaction, the radially, azimuthally, and spirally polarized eigen-modes for the light field are revealed to be of a fundamental interest to describe the physical mechanisms at work when dealing with scalar and vectorial optical singularities. In addition, we also report on nontrivial effects arising from cylindrical symmetry breaking, e.g. tilting the incident beam with respect to the crystal optical axis.

Extreme spin-orbit coupling in crystal-traveling paraxial beams.

The dynamics of the spin-orbit coupling in elegant and standard Hermite-Gaussian (HG), Laguerre-Gaussian (LG), and Bessel-Gaussian (BG) beams propagating through a uniaxial crystal are analyzed. We consider the structure of the electric fields of the paraxial beams and show that the extreme values of the spin and orbital angular momenta are inherent in the elegant HG and LG of high orders. The spin-orbit coupling in the BG beam of the lowest order can result in nearly 100% energy transport from a vortex-free beam to the vortex-bearing beam at a relatively small crystal length. The extreme spin-orbit coupling does not manifest itself in standard HG and LG beams.

Nondiffracting vortex-beams in a birefringent chiral crystal.

A vector-wave analysis of nondiffracting beams propagating along a birefringent chiral crystal for the case of tensor character of both the optical activity and linear birefringence is presented. We have written characteristic equations and found propagation constants and amplitude parameters of the eigenmodes. The characteristic curves have anomalous zones described by an isotropic point or a gap-point, provided that the elements of an optical activity tensor obey the requirement g(11)g(33)<0, |g(33)|>|g(11)|. In the anomalous zone, a nondiffracting beam can propagate through a purely chiral crystal as if through an isotropic medium. We have shown that the field of eigenmodes is nonuniformly polarized in the beam cross section, while the field with the initially uniform polarization distribution experiences periodic transformations. We have revealed that even a purely chiral crystal without linear birefringence can generate optical vortices in an initially vortex-free Bessel beam.