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Focusing a cylindrical vector beam and the Hall effect
V.V. Kotlyar 1,2, S.S. Stafeev 1,2, A.A. Kovalev 1,2, V.D. Zaitsev 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, 1400 kB

DOI: 10.18287/2412-6179-CO-1356

Pages: 47-52.

Full text of article: Russian language.

Abstract:
Polarization of a higher-order cylindrical vector beam (CVB) is known to be locally linear. The higher the beam order, the larger number of full circles the local linear polarization vector makes around the optical axis. It is also known that the CVB with radially symmetric amplitude has zero spin angular momentum (SAM) and zero orbital angular momentum (OAM) both in the initial plane and in the focal plane (because in both Cartesian components of the vector field, the angular derivative of phase is zero). We show here that near the focal plane of the CVB (i.e. before and beyond the focus), an even number of local subwavelength areas with rotating polarization vectors are generated. In addition, in the neighboring areas, the polarization vectors are rotating in the opposite directions. Thus, the longitudinal components of the SAM vector in such neighboring areas are of different sign. After passing through the focal plane, the rotation direction of the polarization vector at each point of the beam cross-section changes to the opposite one. Such a spatial separation of the left and right rotation of the polarization vectors is a manifestation of the optical spin Hall effect.

Keywords:
spin Hall effect, cylindrical vector beam, tight focusing, spin angular momentum, orbital angular momentum.

Citation:
Kotlyar VV, Stafeev SS, Kovalev AA, Zaitsev VD. Focusing a cylindrical vector beam and the Hall effect. Computer Optics 2024; 48(1): 47-52. DOI: 10.18287/2412-6179-CO-1356.

Acknowledgements:
This work was partly funded by the Russian Science Foundation (Project No. 23-12-00236, theoretical background) and within the government project of the Federal Scientific Research Center "Crystallography and Photonics" of the Russian Academy of Sciences (numerical simulation).

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