Electromagnetic theory of reflaxicon fields

The electromagnetic field generated by a right-angle reflective axicon (reflaxicon) is evaluated, in the neighbourhood of the optical axis (the focal line), assuming coherent plane-wave illumination. For a linearly polarized incident wave, the distributions of the electric and the magnetic energy density are found to be rotationally non-symmetric, whereas the total electromagnetic energy density is symmetric. Rotationally symmetric distributions of the electric and magnetic energy densities are obtained with a circularly polarized incident plane wave. The reflaxicon field is also shown to be a striking example of the failure of the pointwise interpretation of the time-averaged Poynting vector as a measure of energy flow: is shown to point in the direction of the optical axis, although the wavevectors of all plane wave components of the reflaxicon field are perpendicular to this axis.