Optical Helicity of Light in the Tight Focus

Using the Richards–Wolf formalism, we obtain explicit analytical expressions for optical helicity density at tight focus of four different light beams: a linearly polarized vortex, an vortex with right-handed circular polarization, superposition cylindrical vector beam and beam, hybrid circular-azimuthal polarization. We show that, in all cases, is nonzero has signs focal plane areas. If changes sign, then full (averaged over cross section focus) zero conserved upon propagation. reveal that when longitudinal component spin angular momentum zero. does not change sign focus, such as circularly it equal to intensity being power conserving Although related polarization state distribution across are found be from those beams interest.