Generation of double-charged optical vortices on the basis of electro-optic Kerr effect

We show that double-charged optical vortices can be generated with the help of Kerr electro-optic effect in either single crystals or isotropic media, including gaseous and liquid ones. We analyze possibilities for the vortex generation via the Kerr effect for different point groups of symmetry and formulate the appropriate conditions. We prove that the crystals, textures, and the isotropic media most suitable for the generation of double-charged optical vortices should belong to the symmetry groups 622, 6mm, 6/mmm, 6, 6/m, ∞/m, ∞, ∞2, ∞mm, ∞/mmm, ∞/∞/mmm, and ∞/∞2.