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Generalized q-plates and novel vector beams

We generalized the conventional concept of q-plate, allowing in its definition non linear 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 (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 non-linearities in the azimuthal variable, the central singularity of the polarization field of a vector beam may bifurcate in several singularities of lower topological charge, preserving the total charge. Depending on the chosen q-plate function, different particular behaviours on the output beam are observed, which offers a whole range of possibilities for creating novel vector beams, as well as polarization critical points and singularity distributions.