Angular momentum switching and orthogonal field construction of C-points

In this Letter, we take on the non-trivial problem of transforming a C-point singularity into its orthogonal state by switching its angular momentum components. For homogeneous distribution, orthogonal transformation is a trivial operation using a single half-wave plate. For C-point singularity, this entails a change in the handedness without disturbing the index, followed by rotation of the state of polarizations in the distribution. Swapping the spin angular momentum (SAM) components of C-point singularities leads to index and handedness inversion, whereas, switching of orbital angular momentum (OAM) components results only in handedness inversion. By changing the SAM and OAM components in sequence, a C-point can be transformed into its orthogonal state. While experimentally demonstrating this, a spiral phase plate, which is a phase element, is shown to perform polarization transformation operation.