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Toroidal polarization vortices in tightly focused beams with singularity
S.S. Stafeev 1,2, V.V. Kotlyar 1,2

IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 960 kB

DOI: 10.18287/2412-6179-CO-734

Pages: 685-690.

Full text of article: Russian language.

In this paper, we numerically investigated tight focusing of cylindrical vector beams of the sec-ond order using Richards-Wolf formulae. It was shown that intensity rings where the Poynting vector was equal to zero appeared not only in the focal plane but also in nearby planes. For example, a lens with numerical aperture NA=0.95 was shown to generate periodical toroidal vortices with a 0.8-mkm period along the z-axis at a distance of about 0.45 mkm from the axis. The vortices were generated pairwise, with the closest-to-focus vortex having clockwise helicity and the subsequent being anti-clockwise. The vortices were also characterized by saddle points. When focusing an optical beam passed through a narrow annular aperture, no toroidal vortices were observed.

tight focusing, Richards-Wolf formulae, energy backflow, toroidal vortices.

Stafeev SS, Kotlyar VV. Toroidal polarization vortices in tightly focused beam with singularity. Computer Optics 2020; 44(5): 685-690. DOI: 10.18287/2412-6179-CO-734.

:The work was partially funded by the Russian Science Foundation under project # 18-19-00595 (Section "Richards-Wolf formulas for narrow angular aperture"), by the Russian Foundation for Basic Research under project ## 18-07-01122, 18-07-01380, 18-29-20003 (Section "Numerical simulation for polarization vortex" and by the Russian Federation Ministry of Science and Higher Education within a state contract with the "Crystallography and Photonics" Research Center of the RAS (Section "Introduction").


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