Gaussian beams with multiple polarization singularities

In recent years, alongside light beams with phase singularities (so-called optical vortices), polarization vortices (including beams with radial and azimuthal polarization) have also been studied. In this work, we analyze paraxial Gaussian beams that have an array of arbitrarily located polarization singularities. A closed analytical expression to describe their complex amplitude is derived. A particular case of singularities localized at the vertices of a regular polygonal is discussed. If the beam has one or two singularities, these points will have radial polarization. If, however, there are four singularities, two of them will be characterized by azimuthal polarization. As the beam propagates, the polarization singularities found in the initial plane are shown to reoccur only in a discrete set of planes, unlike phase singularities, which occur at any transverse plane. In the case of two singularities, radial polarization in the initial plane is found to convert into azimuthal polarization in the far-field. The research findings may find uses in optical data transmission.