Vectorial beam generation with a conical refractive surface

We propose to use a refractive conical axicon for generating azimutally polarized beams. We investigate polarization states of optical rays passing through an interface between optical media, and also polarization transformation with a refractive axicon. We develop a software for raytracing which correctly processes polarization states of the rays and visualizes ellipses of polarization. The polarization state is described in the Jones notation and based on the energy conservation law. We derive and implement formulas for calculating the Jones vector in different bases, as well as transferring the Jones vector from one basis to another. Algorithms for displaying polarization ellipses on one plane for beams that are not plane-parallel have been developed. Ray paths in a three-dimensional axicon are calculated and shown with due regard for polarization.