L}^{\rm ext}={\bf R}\times {\bf P}~,~~{\bf L}^{\rm int}={\bf L} - {\bf L}^{\rm ext}~.$$ Equations (\[eqn:10\])–(\[eqn:14\]) contain all the main observable results related to the AM and SOI of light. First, the $\sigma$-dependent non-paraxial Berry-phase term in ${\bf L}$ should be associated with the *spin-to-orbit AM conversion* [@Li; @Beksh; @AMC1; @AMC2; @Oscar]. Particular cases of this term have appeared in [@BA; @Li; @Beksh]. Second, the *orbital* [@OHE1; @OHE2; @OHE3; @OHE4] and *spin* [@SHE1; @SHE2; @Half; @Aiello] *Hall effects of light* are described by the two terms in the position of the center of gravity, Eq. (\[eqn:12\]). Indeed, for a symmetric vortex beam propagating along the $z$-axis, the transverse coordinates of the center of gravity vanish, $(X,Y)=0$, after integration over $\phi$, but any asymmetry of the field distribution along, say, the $x$-axis immediately causes an $\ell$- and $\sigma$-dependent shift along the orthogonal $y$-axis, $Y\neq 0$ together with tilt $P_x\neq 0$ (see the example in Section IV).

We emphasize that our results (\[eqn:6\])–(\[eqn:14\]) are *exact* and no approximations were made. They are equivalent to application of the canonical operators ${\bf \hat L}$, ${\bf \hat S}$, and ${\bf \hat r}$ to the laboratory-frame field components $( {\tilde E_x ,\tilde E_y ,\tilde E_z } )^T$ supplied 