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Stokes and skyrmion tensors and their application to structured light

Stephen M. Barnett, Sonja Franke-Arnold, Fiona C. Speirits

Abstract

We replace the familiar Stokes vector by a tensor. This allows us to introduce, for example, polar-coordinate components of the Stokes vector. From the tensor we can derive the skyrmion field for mapping the polarization in structured light beams. These ideas have wider application in optics and in electromagnetic theory. We illustrate this with an example from non-paraxial optics and for Poynting's vector.

Stokes and skyrmion tensors and their application to structured light

Abstract

We replace the familiar Stokes vector by a tensor. This allows us to introduce, for example, polar-coordinate components of the Stokes vector. From the tensor we can derive the skyrmion field for mapping the polarization in structured light beams. These ideas have wider application in optics and in electromagnetic theory. We illustrate this with an example from non-paraxial optics and for Poynting's vector.

Paper Structure

This paper contains 11 sections, 47 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminary details
  3. Stokes parameters
  4. Skyrmions
  5. Tensors
  6. Stokes and skyrmion tensors
  7. Polarization beyond paraxial optics
  8. Skyrmions beyond polarization
  9. Skyrmion field based on Poynting's vector
  10. Skyrmion field for Newtonian gravity
  11. Conclusion

Figures (1)

  • Figure 1: a) Polarisation pattern for an $n=1$ skyrmion, with the intensity profile encoded as opacity, and the local polarisation as colour map. The insets show the corresponding Poincaré sphere together with its unwrapped colour map. b) Spatial variations of the Cartesian Stokes parameters (left column), and of the corresponding Stokes tensors in cylindrical polar coordinates (right column).