Note on the helicity decomposition of spin and orbital optical currents

In the helicity representation, the Poynting vector (current) for a monochromatic optical field, when calculated using either the electric or the magnetic field, separates into right-handed and left-handed contributions, with no cross-helicity contributions. Cross-helicity terms do appear in the orbital and spin contributions to the current. But when the electric and magnetic formulas are averaged ('electric–magnetic democracy'), these terms cancel, restoring the separation into right-handed and left-handed currents for orbital and spin separately.