  Helicity $H$, chirality $C$, and spin angular momentum $\mathbf{S}$ are three
physical observables that play an important role in the study of optical
fields. These quantities are closely related, but their connection is hidden by
the use of four different vector fields for their representation, namely, the
electric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$, and the two
transverse potential vectors $\mathbf{C}^\perp$ and $\mathbf{A}^\perp$.
Helmholtz's decomposition theorem restricted to solenoidal vector fields,
entails the introduction of a bona fide inverse curl operator, which permits
one to express the above three quantities in terms of the observable electric
and magnetic fields only. This yields clear expressions for $H, C$, and
$\mathbf{S}$, which are automatically gauge-invariant and display
electric-magnetic democracy.
