Vector Laguerre-Gauss beams with polarization-orbital angular momentum entanglement in a graded-index medium.

It is shown that the vector-vortex Laguerre-Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams with nonzero azimuthal and radial indices in a cylindrical graded-index waveguide is investigated. The wave shape variation with distance taking into account the spin-orbit and nonparaxial effects is analyzed. The effect of long-term periodic revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated. High efficiency transfer of a strongly focused spot through an optical waveguide over large distances takes place with a period of revival.