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Orbital angular momentum density distribution at the sharp focus of vector light fields
V.V. Kotlyar1,2, A.A. Kovalev1,2, A.G. Nalimov1,2, A.M. Telegin2

1 Image Processing Systems Institute, NRC "Kurchatov Institute", Molodogvardeyskaya Str. 151, Samara, 443001, Russia;
2 Samara National Research University, Moskovskoye Shosse 34, Samara, 443086, Russia

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DOI: 10.18287/COJ1719

Article ID: 1719

Language: Russian

Abstract:
In this work, we obtained explicit analytical expressions for the density of the longitudinal projection of the orbital angular momentum vector. These expressions were analyzed in the plane of a sharp focus of four light fields with uniform and non-uniform polarizations: an optical vortex with elliptical polarization, a superposition of a cylindrical vector beam and a beam with linear polarization, an optical vortex with cylindrical polarization, and a beam with non-uniform elliptical polarization. All orbital angular momentum densities for these four fields were found to depend on the polarization state of the initial light field. For two light fields with hybrid polarization, the orbital angular momentum density at the focus was revealed to change sign with a change in both the azimuthal and radial coordinates. It is known that in the case of paraxial optical vortices with elliptical polarization, the orbital angular momentum density does not depend on the polarization state, and is completely determined by the topological charge of the optical vortex. Therefore, in the paraxial case, the azimuthal orbital energy flux always swirls in one direction determined by the sign of the optical vortex topological charge. However, for non-paraxial light fields, the orbital angular momentum density at the focus was shown in this work to depend on the polarization state, so that the energy flow can swirl in different directions at different distances from the optical axis.

Keywords:
orbital angular momentum, topological charge, optical vortex, energy flow.

Acknowledgements:
The work was partly funded by the Russian Science Foundation under grant #26-12-0011 (Theoretical analysis) and NRC "Kurchatov Institute" under a government project (Numerical simulation).

Citation:
Kotlyar VV, Kovalev AA, Nalimov AG, Telegin AM. Orbital angular momentum density distribution at the sharp focus of vector light fields. Computer Optics 2026; 50(3): 1719. DOI: 10.18287/COJ1719.

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