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Computer Optics, 2019, Volume 43, Issue 3, Pages 337–346 (Mi co652)  

OPTO-IT

Sharp focusing of a light field with polarization and phase singularities of an arbitrary order

V. V. Kotlyarab, S. S. Stafeevab, A. A. Kovalevab

a Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia
b IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, Russia

Abstract: 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).

Keywords: sharp focusing, Richards-Wolf formulae, optical vortex, topological charge, phase singularity, polarization singularity, Poynting vector, reverse flux of energy, focal spot symmetry.

Funding Agency Grant Number
Russian Science Foundation 18-19-00595
Russian Foundation for Basic Research 18-29-20003 ìîë_à
Ministry of Science and Higher Education of the Russian Federation 007-ÃÇ/×3363/26
The work was partly funded by the Russian Science Foundation under grant # 18-19-00595 (section “Light field with a phase and polarization singularity in the focus of an aplanatic system”), the Russian Foundation for Basic Research under grant # 18-29-20003 (section “Simulation of sharp focusing of an optical vortex with high-order radial and azimuthal polarization”), and the RF Ministry of Science and Higher Education within a state contract with the “Crystallography and Photonics” Research Center of the RAS under agreement 007-ÃÇ/×3363/26 (section “Partial cases from the general expression”).


DOI: https://doi.org/10.18287/2412-6179-2019-43-3-337-346

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Received: 12.03.2019
Accepted:08.05.2019

Citation: V. V. Kotlyar, S. S. Stafeev, A. A. Kovalev, “Sharp focusing of a light field with polarization and phase singularities of an arbitrary order”, Computer Optics, 43:3 (2019), 337–346

Citation in format AMSBIB
\Bibitem{KotStaKov19}
\by V.~V.~Kotlyar, S.~S.~Stafeev, A.~A.~Kovalev
\paper Sharp focusing of a light field with polarization and phase singularities of an arbitrary order
\jour Computer Optics
\yr 2019
\vol 43
\issue 3
\pages 337--346
\mathnet{http://mi.mathnet.ru/co652}
\crossref{https://doi.org/10.18287/2412-6179-2019-43-3-337-346}


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