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Skyrmion number for a generalized vector Poincaré beam
V.V. Kotlyar 1,2, A.A. Kovalev 1,2, A.M. Telegin 2

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

 PDF, 1056 kB

DOI: 10.18287/2412-6179-CO-1507

Pages: 5-12.

Full text of article: Russian language.

Abstract:
We investigate two initial vector Poincaré-type light fields that can be treated as optical skyrmions – topological quasiparticles. For such fields, explicit expressions are obtained for the components of a 3D-vector skyrmionic field in the initial plane as well as for the skyrmion numbers, proportional to the topological charges of the optical vortices constituting the Poincaré beams. A new constructive formula is derived for effective calculation of the skyrmion number via the components of the normalized Stokes vector, rather than via the components of the vector skyrmion field. The skyrmion numbers computed by the well known and new formulae coincide. We also show that each component of the 3D-vector skyrmion field has a number equal to one third of the full skyrmion number. The numerical simulation results are consistent with the theoretical conclusions.

Keywords:
quasiparticle, optical skyrmion, Poincaré beam, optical vortex, Stokes vector, skyrmion number.

Citation:
Kotlyar VV, Kovalev AA, Telegin AM. Skyrmion number for a generalized vector Poincaré beam. Computer Optics 2025; 49(1): 5-12. DOI: 10.18287/2412-6179-CO-1507.

Acknowledgements:
This work was partly funded by the Russian Science Foundation under project No. 23-12-00236 (Theory and Numerical simulation) and within a government project of the NRC "Kurchatov Institute" (Introduction and Conclusion).

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