On the Helicity of Radiative Electromagnetic Fields

We derive relativistically invariant expressions for the magnetic and electric helicities of free electromagnetic field through the currents, which created those field. We demonstrate that, for radiative fields (e.g., laser pulses), both helicities are conserved and equal to each other. Moreover, the conservation of the helicity means that, in radiative electromagnetic fields, the electric and magnetic vectors are always orthogonal to each other. Proceeding to the quantum theory, we show that the corresponding quantum helicity field operator is equal to the sum of projections of spins of all photons onto their momenta. Finally, as an example, we obtain and discuss the expressions for the total helicity, number of photons, and the total spin momentum of the field of a dipole electromagnetic pulse.