Abstract
In this article, we propose a simple method to generate purely transverse spin density in a high numerical aperture system, and it is realized by focusing an amplitude tailored beam with a dipole-like shape. Through our analytical analysis, it is found that in this focused field the purely transverse spin density is not only confined in the focal plane, but also can exist in two mutually perpendicular meridional planes. Especially, the fields with purely transverse spin density are also examined from the view of topology. Two typical topological events which usually happen in traditional two dimensional transverse fields are observed in the meridional plane with purely transverse spin density, and it shows that the ‘photonic wheels’ follow the rule of topological index in their topological reactions. To the best of our knowledge, it is the first time to test the topological behavior of the field with purely transverse spin density. Our finding not only supplies a simple way to generate ‘photonic wheels’ in three planes of the field, but also adds new features to the field containing ‘photonic wheels’.
Highlights
Light can possess both spin and orbital angular momenta (SAM and OAM) which are associated with circular polarization and optical vortex, respectively
In this article, we propose a simple method to generate purely transverse spin density in a high numerical aperture system, and it is realized by focusing an amplitude tailored beam with a dipole-like shape
Through adapting the traditional 2D Stokes parameters, to the best of our knowledge, it is the first time of observation of topological reaction for the ‘photonic wheels’ in the plane containing the propagation direction
Summary
Light can possess both spin and orbital angular momenta (SAM and OAM) which are associated with circular polarization and optical vortex, respectively. In light fields within nonparaxial regime, like strongly focused fields or near field, the longitudinal component of the field cannot be negligible, i.e. the field is three dimensional (3D) In such 3D fields, the transverse component of the spin density exists and the orientation of the ‘spin density vector’ can be arbitrary in 3D space [8]–[10], leading to interesting structures of 3D fields, such as spiral spin density vectors [11]–[13], polarization Möbius strip [14]–[16] and topological knots [17], [18]. Since the SAM and the spin density have a close relation with the C points, and purely transverse spin density reflects the field with polarization ellipses lying in 2D meridional planes, it will be very interesting to examine these ‘photonic wheels’ in the view of topology. In this article, we will examine the topological reactions in the field with purely transverse spin density, and as it will be shown that the two typical topological events occur for the ‘photonic wheels’
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