Alexander V. Volyar

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.

Generation of higher-order optical vortices by a dielectric wedge

Diffraction of a Gaussian beam with a system of successively located optical wedges is considered. It is shown that the system is able to form higher-order optical vortices.

Determination of topological charges of polychromatic optical vortices

We introduce a simple, single beam method for determination of the topological charge of polychromatic optical vortices. It is based on astigmatic transformation of singular optical beams, where the intensity pattern of a vortex beam acquires a form of dark stripes in the focal plane of a cylindrical lens. The number of the dark stripes is equal to the modulus of the vortex topological charge, while the stripe tilt indicates the charge sign. We demonstrate experimentally the effectiveness of this technique by revealing complex topological structure of polychromatic singular beams.

Generation of single-charge optical vortices with an uniaxial crystal

We implement a novel experimental technique for generating mono- and polychromatic optical beams with on-axis single vortex by manipulating polarization singularities of light in birefringent crystals. We demonstrate that, in contrast to the well-known optical quadrupoles generated by beams propagating along the optical axis of a uniaxial crystal, the beam bearing isolated single-charge on-axis vortex can be generated if the incident beam is tilted with respect to the optical axis at a certain angle.

Focusing and correlation properties of white-light optical vortices.

We generate double-charge white-light optical vortices by sending a circularly polarized partially incoherent light through an uniaxial crystal. We show that the generated polichromatic vortices are structurally stable, and their correlation properties can be altered by the beam focusing, resulting in changes of the vortex core visibility.

Quadrefringence of optical vortices in a uniaxial crystal

The splitting of a single optical vortex into four separate ones in a singular beam is theoretically and experimentally described for the propagation of obliquely incident light in a uniaxial crystal. We also find the condition under which the generated vortices in each of the four individual beams propagate independently without changing their structure and have different locations in all beams for any crystal lengths.

The formation of optical vortices in the course of light diffraction on a dielectric wedge

It is theoretically and experimentally demonstrated that diffraction of a fundamental Gaussian beam at the edge of a dielectric wedge leads to the formation of a chain of optical vortices in the far wave zone. The conditions of phase synchronism are established under which a single optical vortex possessing the ideal shape is generated. A special mathematical approach is developed for description of the character of vortex distortion, which is analogous to the Jones column vector formalism used to describe the polarization of light. It is found that the plots of the degree of vortex ellipticity versus wedge angle and Gaussian beam waist radius exhibit pronounced peaks corresponding to the phase synchronism. The experimental and theoretical results are compared. The experimentally observed vortex ellipticity Q=0.93 at a diffraction efficiency of 0.98 is evidence that the proposed method has good prospects for implementation in real fiber-optic sensors of physical parameters employing optical vortices.

The structure of a nonparaxial Gaussian beam near the focus: II. Optical vortices

Exact analytical solutions of Maxwell’s equations describing the behavior of a nonparaxial optical vortex in the vicinity of a focal waist are obtained using the Whittaker method of scalar potentials, the point complex source method, and approximate Davis boundary conditions. It is shown that nonparaxial optical vortices in free space fall into three large groups: even and odd vortices with preferential circular polarization and azimuthally symmetric TE and TM vortices. The fields of even and odd nonparaxial vortices agree well with the fields of guided homogeneous and inhomogeneous vortices of a weakly guiding fiber. In the paraxial approximation, the expressions obtained for the fields are transformed to the fields of paraxial optical vortices. In the focal region, a nonparaxial beam experiences elliptic deformation of the cross section. This elliptic deformation is shown to result from the asymmetric location of regions with negative energy flows. The reversal of sign of the topological charge and the helicity of a combination of even and odd vortices causes both rotation of the dislocation axis through π/2 and longitudinal displacement of the focal spot, which are the transverse and the longitudinal optical Magnus effects.

Optical vortex generation and Jones vector formalism

Physical phenomena accompanying the generation and propagation of a single optical vortex caused by the diffraction of a Gaussian beam by the edge of a dielectric wedge is studied theoretically and experimentally.

Symmetric array of off-axis singular beams: spiral beams and their critical points.

We consider conditions of structural stability under which the array of singular beams preserves its topological structure and intensity distribution while slightly perturbing its intrinsic parameters. The orbital angular momentum of the array as a function of the array parameters is a characteristic function, and its extreme points correspond to stable and unstable array states.