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Spectrum of optical vortices at the focus of a vortex beam
A.A. Kovalev1,2

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/COJ1709

Article ID: 1709

Language: Russian

Abstract:
Based on the Richards-Wolf formulas, analytical expressions are obtained for the spectrum of optical vortices at the focus of a vortex beam with elliptical polarization. The spectrum is found to be independent of the phase of the focused field. It is also revealed that the polarization of the field affects only the spectrum asymmetry but not the distribution between the main and secondary components. On the contrary, the spectrum asymmetry does not depend on the radial amplitude of the focused field, but the energy fractions that go to the main and secondary components do. Quadratic inequalities are obtained that allow one to assess the possibility of obtaining a specific spectrum of optical vortices by constraining the initial field with an annular diaphragm.

Keywords:
optical vortex, sharp focusing, elliptical polarization, orbital angular momentum spectrum, Richards-Wolf formulae, annular aperture.

Acknowledgements:
The work was partly funded by the Russian Science Foundation under grant 26-12-00117 (Theory). Part of this work was performed within the government project of NRC "Kurchatov Institute" (Numerical simulation).

Citation:
Kovalev AA. Spectrum of optical vortices at the focus of a vortex beam. Computer Optics 2026; 50(3): 1709. doi:10.18287/COJ1709.

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