a superposition of $\sigma =\pm 1$ beams (\[eqn:41\]) we obtain [@R1]: $$\label{eqn:42}
{L_z } =  \ell  + \bar \sigma \frac{\Phi _B }{2\pi },~
{S_z } = \bar \sigma \left( {1 - \frac{\Phi _B }{2\pi }} \right),~
{J_z } = \ell  + \bar \sigma.$$ Here $\bar \sigma  = ( {\left| {A^ +  } \right|^2  - \left| {A^ -  } \right|^2 } )/( {\left| {A^ +  } \right|^2  + \left| {A^ -  } \right|^2 } )$ is the averaged helicity and $$\label{eqn:43}
\Phi _B  = \oint\limits_{\rm C} {{\bf A}_B  \cdot d{\bf k}}  = 2\pi \left( {1 - \cos \theta _0 } \right)$$ is the Berry phase associated with the contour ${\rm C}=\{\theta=\theta_0, \phi\in(0,2\pi)\}$ formed by the ${\bf k}$-vectors distribution on the sphere of directions, Fig. 1(a) [@GP]. The Berry phase is equal to the flux of the monopole field $\mathbf{F}_B  = \partial _\mathbf{k}  \times \mathbf{A}_B  = \mathbf{k}/k^3$ through the area of the ${\bf k}$-space sphere bounded by the contour ${\rm C}$. In this manner, the $\bar\sigma$-dependent term in $L_z$ represents a monopole-flux contribution to the OAM, cf. Eq. (87) in [@SUSY]. In the paraxial limit the Berry-phase terms vanish as $\Phi _B  \simeq \pi \theta _0^2  \to 0$. The values (\[eqn:42\]) evidence 