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<p>We discuss two source vector fields of Poincare-beam type that can be looked upon as optical skyrmions, i.e. topological quasiparticles. We derive explicit analytical relationships that describe projections of a three-dimensional (3D) skyrmion vector field in the source plane and skyrmion numbers, which are shown to be proportional to the topological charges of constituent optical vortices of the Poincare beams. We also propose a new constructive formula as an effective tool for calculating the skyrmion number via normalized Stokes vector projections rather than skyrmion vector field projections. The skyrmion numbers calculated using the familiar and newly proposed formulae coincide. Numbers of each projection of a 3D skyrmion vector field are shown to comprise a third of the full skyrmion number. The theoretical conclusions are validated by a numerical simulation.</p>

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The optical skyrmion numbers

  • 期刊论文

  • 发表日期：

    2025年5月19日

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  • V. V. Kotlyar,
  • A. A. Kovalev,
  • A. M. Telegin

摘要

We discuss two source vector fields of Poincare-beam type that can be looked upon as optical skyrmions, i.e. topological quasiparticles. We derive explicit analytical relationships that describe projections of a three-dimensional (3D) skyrmion vector field in the source plane and skyrmion numbers, which are shown to be proportional to the topological charges of constituent optical vortices of the Poincare beams. We also propose a new constructive formula as an effective tool for calculating the skyrmion number via normalized Stokes vector projections rather than skyrmion vector field projections. The skyrmion numbers calculated using the familiar and newly proposed formulae coincide. Numbers of each projection of a 3D skyrmion vector field are shown to comprise a third of the full skyrmion number. The theoretical conclusions are validated by a numerical simulation.