We introduce a wide class of singular inhomogeneously polarized beams characterized by a nonuniform rotation rate of the local polarization azimuth about a C- or a V-point. They are obtained by adding an extra phase modulation with an m-fold rotational symmetry to the helical wavefronts underpinning Poincaré beams. The resulting modulated Poincaré beams have been theoretically studied and experimentally generated using tailored space-varying-axis plates based on liquid crystals.

Asymmetric polarization disclinations, such as monstars, can be generated in two distinct ways: (i) by an inseparable superposition of three spatial modes bearing optical vortices with circular polarization states; (ii) by using a modulated Poincaré beam, consisting of an inseparable superposition of the same circular polarization states with the fundamental Gaussian beam TEM00 and a single scalar beam exhibiting an azimuthally modulated vortex with an m-fold rotational symmetry. Based on the analysis of the spatial modes indirectly involved into the mix through the latter method, we investigate its capability of spanning as many disclinations as possibile, as well as its capability of enabling effective predictions about the generated patterns, such as relevant geometric features, at the early design stage.

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