Hidden singularities in 3D vector fields

In this article we show that in a three dimensional (3D) optical vector field there exist two types of hidden singularities, one is spin density (SD) phase singularity and the other is SD vector singularity, which are both unique to 3D fields. The nature of these SD singularities is discussed and their connection with traditional optical singularities is also examined. Especially it is shown that in a 3D field with purely transverse SD ('photonic wheels'), these two types of singularities exhibit very interesting behaviors: they are exactly mapped to each other regardless of their different physical meanings and different topological structures. Our work supplies a fundamental theory for the SD singularities and will provide a new way for further exploration of 3D vector fields.