Energy rule for enhancing the spin Hall effect in superposition of axisymmetric beams with cylindrical and linear polarization

We study the spin angular momentum of a superposition of two vector light beams radial symmetry, one has cylindrical polarization and another – linear. Both beams can have an arbitrary radial shape. An analytical expression is obtained for the spin angular momentum and two its properties are proven. The first one is that changing weight coefficients of the superposition does not changes the shape of the spin angular momentum density distribution, whereas the intensity shape can change. The second property is that the maximal spin angular momentum density is achieved when both constituent beams in the superposition have equal energy.