  In this article we show that in a three dimensional (3D) optical field there
can 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 spin density (`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 may provide a new way for further exploration of
3D optical fields.
