Photonic Wheels and Their Topological Reaction in a Strongly Focused Amplitude Tailored Beam

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'.