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Helicity $H$, chirality $C$, and spin angular momentum $\mathbf{S}$ are threephysical observables that play an important role in the study of opticalfields. These quantities are closely related, but their connection is hidden bythe use of four different vector fields for their representation, namely, theelectric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$, and the twotransverse 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 permitsone to express the above three quantities in terms of the observable electricand magnetic fields only. This yields clear expressions for $H, C$, and$\mathbf{S}$, which are automatically gauge-invariant and displayelectric-magnetic democracy.

Helicity, chirality and spin of optical fields without vector potentials