Needles of light produced with a quasi-parabolic mirror.

Abstract

We propose a quasi-parabolic mirror that can produce a long needle of light by focusing a radially polarized annular beam. The quasi-parabolic mirror can be acquired by moving the axis of rotation of a parabolic mirror. Using the extended Richards-Wolf theory for axisymmetric surfaces, we calculated that the needle obtained can have a longitudinal FWHM over hundreds to thousands of wavelengths by keeping the transverse FWHM under 0.36λ. The consistent expression of the approximate relationship between the angular thickness of the incident beam and the longitudinal FWHM based on both geometrical optics and wave optics is presented.