Paraxial and non-paraxial optical skyrmions

Vector light beams feature a spatially varying optical polarisation and can exhibit localised structures reminiscent of the skyrmions familiar from the study of magnetic media. We present a theory and experimental measurements of such skyrmions in both paraxial and non-paraxial optics. A key feature for our analysis is the transverse skyrmion field which determines the properties of the skyrmions and traces out field lines. In paraxial optics these field lines are lines of constant polarisation, but in non-paraxial optics, the fact the polarisation ellipses are no longer restricted to the transverse plane, makes it necessary to introduce several different skyrmion fields, each representing a different aspect of the three-dimensional optical polarisation.