On the helicity of radiative electromagnetic fields

Abstract: A relativistically invariant expression for the magnetic and electric helicities of free electromagnetic field through the currents, which created those field, are derived. It is demonstrated that for radiative fields (e.g. laser pulses) the 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, it is shown that the corresponding quantum helicity field operator is equal to the sum of projections of spins of all photons onto their momentums. Finally, as an example, the expressions for the total helicity, number of photons and the total spin momentum of the field of a dipole electromagnetic pulse are obtained and discussed.