that the $\sigma$-dependent non-paraxial part of the OAM arises from Berry-phase terms describing the *spin-orbit interaction* (SOI) of light. A similar effect occurs dynamically upon *spin-to-orbital AM conversion* in focusing and scattering of polarized light [@Beksh; @AMC1; @AMC2; @Oscar]. Other manifestations of the SOI are the *spin* [@SHE1; @SHE2; @Half; @Aiello] and *orbital* [@OHE1; @OHE2; @OHE3; @OHE4] *Hall effects of light* (i.e., $\ell$- and $\sigma$-dependent transverse shifts of the field center of gravity) that are described by our position operator and take place even in free space [@Aiello; @OHE4]. We apply the general theory to vector Bessel beams, for which the fundamental operators manifest themselves in immediately observable $\ell$- and $\sigma$-dependent intensity distributions. The exact wave results are also explained in terms of the underlying geometrical-optics rays and caustics.

Operator formalism
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We consider an electromagnetic field in free space, characterized by its plane-wave electric-field spectrum ${\bf \tilde E}\left( {\bf k} \right)$ without evanescent modes. The SOI of light originates from the transversality constraint, ${\bf k} \cdot {\bf \tilde E} = 0$, which couples polarization to the wave vector and reduces the full 3D vector space of the electric field components to the 2D subspace of the components tangential to 