Ellipse field to vector field singularities through diffraction

Ellipse fields and vector fields refer to the electric fields with predominant states of polarization as elliptical and linear, respectively. Singularities in these ellipse fields (C points and L lines) and vector fields (V points) refer to points where some of the parameters related to polarization are not defined. A simple technique for transforming a C point to a V point is suggested by diffracting a higher order integral C points from a fork grating. The fork grating transfers the orbital angular momentum (OAM) in each of the diffraction orders yielding polarization singularities with different OAM and spin angular momentum (SAM) compositions. A V point singularity is obtained in one of the diffracted orders depending on the OAM content in each of the superposing circular basis of the input C point, and the charge of the fork grating. The index of the desired V point and the order in which it occurs can be engineered by appropriately choosing the input C point beam and the charge of the fork grating. Therefore, this diffraction technique can be used for the transformation of an ellipse field singularity to a vector field singularity through just a single element, i.e., a fork grating.