Spin-orbit transformation in a sharp focus

Kotlyar V.V., Kovalev A.A., Nalimov A.G., Kozlova E.S., Telegin A.M.

For Russian citation (Opticheskii Zhurnal):

Котляр В.В., Ковалев А.А., Налимов А.Г., Козлова Е.С., Телегин А.М. Спин-орбитальное преобразование в остром фокусе // Оптический журнал. 2025. Т. 92. № 4. С. 3–13. http://doi.org/10.17586/1023-5086-2025-92-04-3-13

Kotlyar V.V., Kovalev A.A., Nalimov A.G., Kozlova E.S., Telegin A.M. Spin-orbit transformation in a sharp focus [in Russian] // Opticheskii Zhurnal. 2025. V. 92. № 4. P. 3–13. http://doi.org/10.17586/1023-5086-2025-92-04-3-13

For citation (Journal of Optical Technology):

Abstract:

Subject of study. Laser vector vortex beams and their sharp focusing. Spin-orbit transformation effect at a focus. Aim of study. Theoretical study and numerical simulation of features of a spin-orbit effect at a sharp focus for an optical vortex with circular polarization. Method. The study was carried out using the Richards-Wolf method, which is based on Debye integrals. Main results. The transverse and longitudinal projections of Poynting vectors (energy flow), spin angular momentum, and orbital angular momentum averaged over the beam cross section in the focal plane were obtained. Practical significance. It is shown for the first time that during the spin-orbit transformation, a part of the longitudinal spin angular momentum does not transform (is not transformed) into the longitudinal orbital angular momentum, as it is usually believed. It is shown that the full spin angular momentum is preserved during focusing and is only redistributed: part of the longitudinal component is converted into a transverse (azimuthal) component. The reason for the orbital angular momentum generation at the focus is that a circularly polarized beam generates two optical vortices at the focus: a transverse one with topological charge 2 and a longitudinal one with charge 1. These vortices create an azimuthal energy flow at the focus.

Keywords:

spin angular momentum, spin-orbit transformation, topological charge, orbital angular momentum, Poynting vector

Acknowledgements:

the work was partly supported by the Russian Science Foundation Grant № 23-12-00236 (in part of theory) and within a state contract of the NRC "Kurchatov Institute" (in part of simulation)

OCIS codes: 030.1670

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