Generalized q -plates and alternative kinds of vector and vortex beams

Abstract

We took a generalization of the conventional concept of the q-plate, allowing in its definition nonlinear functions of the azimuthal coordinate, and simulated the resulting fields of applying this kind of element to uniformly polarized input beams, both in the near-field (Fresnel diffraction) and the far-field (Fraunhofer diffraction) approximations. In general terms, when working in the near-field regime, the chosen function defines the output polarization structure for linearly polarized input beams and the phase of the output field for circularly polarized input beams. In the far-field regime, it is obtained that when there are nonlinearities in the azimuthal variable, the central singularity of the polarization field of a vector or vortex beam may divide into several singularities of lower topological charge, preserving the total charge. Depending on the chosen q-plate function, different particular behaviors on the output beam are observed, which offers a whole range of possibilities for creating alternative kinds of vector and vortex beams, as well as polarization critical points and singularity distributions.