Transverse shift of a high-order paraxial vortex-beam induced by a homogeneous anisotropic medium

Abstract

We consider the propagation of a tilted high order paraxial vortex-beam through a homogeneous anisotropic medium of a uniaxial crystal. We found that the initially circularly polarized beam bearing the lorder optical vortex splits into ordinary and extraordinary beams with a complex vortex structure. After a series of dislocation reactions the vortices gather together at the axis of the partial beam with the initial circular polarization shaping the l-order optical vortex. However, only l-1 vortices gather together on the axis of the partial beam with the orthogonal circular polarization. One optical vortex is shifted along the direction perpendicular to the inclination plane of the beam. Such a vortex displacement induces the transverse shift of the partial beam. In fact, we deal with the beam quadrefringence in a uniaxial, homogeneous anisotropic medium. The first two beams is a result of the splitting of the initial tilted beam into the ordinary and extraordinary ones. The appearance of the second two beams is caused by the transverse shift of one of the circularly polarized components in the initially circularly polarized vortex-beam or both circularly polarized components in the initially linearly polarized beam .We consider this effect both in terms of the conservation law of the angular momentum flux along the crystal optical axis and on the base of the solutions to the paraxial wave equation for the initially circularly and linearly polarized beams. We revealed that the transverse shift of the crystal traveling beam depends on neither a magnitude nor a sign of the vortex topological charge being defined only by a handedness of the initial circular polarization and a sign of the inclination angle of the beam. Also we analyze the deformation of the cross-section of the shifted vortex-beams and its evolution as the beam propagates along the crystal.

Improved theory for the polarization-dependent transverse shift of a paraxial light beam in free space

“…Processes in which polarization state affects spatial characteristics of a light beam are known as manifestations of spin-orbital interaction of light [1][2][3][4][5][6][7][8][9][10][11][12][13]. Such effects can take place in the presence of inhomogeneous or anisotropic media [2][3][4][5][6][7][8] as well as in free space [9][10][11][12][13].…”

“…Such effects can take place in the presence of inhomogeneous or anisotropic media [2][3][4][5][6][7][8] as well as in free space [9][10][11][12][13]. One of the most spectacular manifestations of the spin-orbit coupling is a "spin Hall effect of light", a polarization-induced transverse shift of the beam trajectory.…”

Topological defects of optical indicatrix orientation in optically biaxial crystals. The case of light propagation in the directions close to the optic axes

“…Such singularities can be induced by different inhomogeneous fields [14][15][16][17][18][19] under propagation of nearly parallel beams through crystals or glasses. The effect can be observed if conical beams propagate in optically uniaxial crystals along the optic axis (OA) direction [20][21][22][23][24][25]. The same is true for the case of optically biaxial crystals, provided that the beam propagates along one of the OAs under the conditions of conical refraction [26][27][28].…”

Nonparaxial wave beams in a uniaxial birefringent crystal

“…Such a deformation effect represents geometrical manifestation of the interference between nonparaxial wave beams (ordinary and extraordinary) having different spatial scales. Notice that deformation of the pattern does not vanish even in the paraxial case [14,18,24], being inherent to linearly polarised beams. The above results are consistent with the theoretical analysis [18,25,26] for paraxial beams propagating perpendicular or nearly perpendicular to the optic axis in crystals.…”

“…This method has been used for the first time for a tilted propagation of extraordinary Gaussian beam in a uniaxial birefringent crystal (see the work [19]). In the studies [23,24], variations of the above method have been employed for tilted vortex beams of the highest orders.…”