Laguerre-Gaussian beams with complex and real arguments in a uniaxial crystal

Abstract

A solution to the paraxial wave equation for Laguerre-Gaussian beams with complex and real arguments in a uniaxial crystal is found and analyzed. It is shown that the beams with a complex argument form a complete group of the solution, while the beams with a real argument satisfy the equation only for an arbitrary radial index, with the azimuthal index being fixed and equal to l = 1. The evolution of phase singularities is considered by the example of transformation of the structure of topological multipoles and generation of optical vortices.