No abstract

The skyrmion number of paraxial optical skyrmions can be defined solely via their polarization singularities and associated winding numbers, using a mathematical derivation that exploits Stokes's theorem. It is demonstrated that this definition provides a robust way to extract the skyrmion number from experimental data, as illustrated for a variety of optical (Néel‐type) skyrmions and bimerons and multi‐skyrmions. This method generates not only an increase in accuracy, but also provides an intuitive geometrical approach to understanding the topology of such quasi‐particles of light and their robustness against smooth transformations.

An electric field propagating along a non-planar path can acquire geometric phases. Previously, geometric phases have been linked to spin redirection and independently to spatial mode transformation, resulting in the rotation of polarisation and intensity profiles, respectively. We investigate the non-planar propagation of scalar and vector light fields and demonstrate that polarisation and intensity profiles rotate by the same angle. The geometric phase acquired is proportional to j = ℓ + σ, where ℓ is the topological charge and σ is the helicity. Radial and azimuthally polarised beams with j = 0 are eigenmodes of the system and are not affected by the geometric path. The effects considered here are relevant for systems relying on photonic spin Hall effects, polarisation and vector microscopy, as well as topological optics in communication systems.

In the version of this article initially published, there was an error in the expression directly following equation ( 3) where the text now reading "where |v 1 〉=T B |u 1 〉 and |v 2 〉= T B |u 2 〉" appeared initially as "where |v 1 〉 =T B + t 12 |u 2 〉 and |v 2 〉 = T B . " The error has been corrected in the HTML and PDF versions of the article.

An electric field propagating along a non-planar path can acquire geometric phases. Previously, geometric phases have been linked to spin redirection and independently to spatial mode transformation, resulting in the rotation of polarisation and intensity profiles, respectively. We investigate the non-planar propagation of scalar and vector light fields and demonstrate that polarisation and intensity profiles rotate by the same angle. The geometric phase acquired is proportional to j = +σ, where is the topological charge and σ is the helicity. Radial and azimuthally polarised beams with j = 0 are eigenmodes of the system and are not affected by the geometric path. The effects considered here are relevant for systems relying on photonic spin Hall effects, polarisation and vector microscopy, as well as topological optics in communication systems.