  Electromagnetic spins, including longitudinal and transverse ones, have been
playing important roles in light-matter interactions. Here, we formulate a
unified equation to uncover the physical origins and topological properties of
longitudinal and transverse spins in a generic electromagnetic field. The
equation reveals universally that the transverse spin is locked with the
kinetic momentum and originated from the transverse inhomogeneities of field,
whereas the helix-dependent longitudinal spin orients parallel to the local
wavevector. Remarkably, a hidden extraordinary helix-dependent transverse spin
possessing helix-dependent spin-momentum locking is discovered and the number
of locking states consistent with the nontrivial topological spin Chern number.
Furthermore, this spin which determines the inverted helical components is
related to the Berry curvature closely. The findings, which are demonstrated
experimentally by measuring the three-dimensional spin components in the
focusing configuration, will deepen the understanding the underlying physics of
spins and open an avenue for chiral quantum optical applications.
