Basis construction using generic orthogonal C-points

Abstract

Transformation of a C-point singularity into its orthogonal state has been introduced recently. This non-trivial process of transformation naturally raises a question about its significance. In this paper we show that orthogonal C-point polarization singularities can be used to construct basis sets of polarization optics. The generic C-points namely lemons and stars are used to substantiate the idea. Here, we show homogeneous polarization distributions as superpositions of two orthogonal C-points. The Wronskian of the two orthogonal basis states is non-zero which indicates that the basis states are linearly independent. This novel idea where homogeneous polarization distributions are expressed as superpositions of singular polarization distributions may be useful in diverse fields beyond polarization optics. This exercise is shown to bring out hitherto unknown interesting structures like interconnections between polarization singularity, phase singularity and stereographic projection, in polarization optics.