Open AccessSharp focusing of a light field with polarization and phase singularities of an arbitrary order
Author(s) -
V. V. Kotlyar,
Sergey S. Stafeev,
Alexey A. Kovalev
Publication year - 2019
Publication title -
kompʹûternaâ optika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 29
eISSN - 2412-6179
pISSN - 0134-2452
DOI - 10.18287/2412-6179-2019-43-3-337-346
Subject(s) - poynting vector , physics , optical vortex , polarization (electrochemistry) , optics , cardinal point , optical axis , vortex , singularity , topological quantum number , circular polarization , magnetic field , ray , electric field , quantum mechanics , geometry , lens (geology) , beam (structure) , chemistry , mathematics , thermodynamics
Using the Richards-Wolf formalism, we obtain general expressions for all components of the electric and magnetic strength vectors near the sharp focus of an optical vortex with the topological charge m and nth-order azimuthal polarization. From these equations, simple consequences are derived for different values of m and n. If m=n>1, there is a non-zero intensity on the optical axis, like the one observed when focusing a vortex-free circularly polarized light field. If n=m+2, there is a reverse flux of light energy near the optical axis in the focal plane. The derived expressions can be used both for simulating the sharp focusing of optical fields with the double singularity (phase and polarization) and for a theoretical analysis of focal distributions of the intensity and the Poynting vector, allowing one to reveal the presence of rotational symmetry or the on-axis reverse energy flux, as well as the focal spot shape (a circle or a doughnut).