Inhomogeneous polarization distributions can host polarization singularities such as lemons, monstars, stars, flowers, spider webs, and higher-order C-points in optical beams. Singularities in ellipse fields are characterized by a C-point index and singularities in vector fields by the Poincare–Hopf index. These singularities can be generated by diffractive or interference methods. In this paper, we show that a half-wave plate (HWP) can be used for polarization singularity index sign inversion. The result presented here is powerful, and it shows the importance of a HWP in the study of polarization singularities. The HWP affects the entire state of polarization (SOP) distribution in the index sign inversion process. The concomitant global change of the SOP distribution happens in an orderly fashion to change the polarity of the polarization singularity index. This method of changing the polarity of the polarization singularity index by a HWP holds good both for ellipse fields as well as for vector fields.
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