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Spin angular momentum at the sharp focus of a cylindrical vector vortex beam
V.V. Kotlyar 1,2, S.S. Stafeev 1,2, A.M. Telegin 1,2

1 IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS,
443001, Samara, Russia, Molodogvardeyskaya 151;
2 Samara National Research University,
443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 439 kB

DOI: 10.18287/2412-6179-CO-1347

Pages: 875-883.

Full text of article: Russian language.

Abstract:
Sharp focusing of a light field with double (phase and polarization) singularity is studied. Using the Richards-Wolf method, an exact analytical expression for the longitudinal projection of the spin angular momentum (SAM) vector at the focus is obtained. The expression derived suggests that 4 (n –1) subwavelength regions are formed at the focus, where n is the cylindrical vector beam order, with their centers located on a certain circle centered on the optical axis. Notably, the SAM projections are found to have the opposite sign in the neighboring regions. This means that in the neighboring focal regions, the light has alternating left or right elliptical polarization (manifestation of a spin Hall effect). At the center of the focal spot near the optical axis, the field is right-handed elliptically polarized at m > 0, or left-handed elliptically polarized at m < 0, where m is the vortex charge. The total longitudinal spin, i.e., the longitudinal SAM component averaged over the beam-cross section, is zero and preserved upon focusing. Due to the beam containing an optical vortex with charge m, the transverse energy flow rotates on a spiral path near the focal plane, rotating on a circle in the focal plane. The rotation direction near the optical axis is counterclockwise for m > 0, and clockwise for m < 0.

Keywords:
spin angular momentum, tight focusing, cylindrical vector beam, optical vortex.

Citation:
Kotlyar VV, Stafeev SS, Telegin AM. Spin angular momentum at the sharp focus of a cylindrical vector vortex beam. Computer Optics 2023; 47(6): 875-883. DOI: 10.18287/2412-6179-CO-1347.

Acknowledgements:
This work was partly funded by the Russian Science Foundation under grant No. 23-12-00236 (Section “Theoretical background”) and the RF Ministry of Science and Higher Education within the government project of the FSRC “Crystallography and Photonics” RAS (Section “Numerical Simulation”).

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