Helicity of Poincaré beams at the sharp focus

In this study, helicity of Poincaré beams was considered from the point of view of the Richards-Wolf formalism. It was shown that helicity for Poincaré beams always has radial symmetry and does not depend on the azimuthal angle of the beam. The absolute value of helicity was shown to be maximum when the polar angle of the beam was zero or π, being zero at the angle π/2. Non-zero values of helicity on the optical axis were observed for beam orders of 0, 1, and 2. If the polar angle of the beam was zero, the intensity of Poincaré beams was revealed to coincide with the helicity up to a factor.