p}={\bf k}$, $\mathbf{\hat r}=i{\partial_{\bf k}}$, ${\bf k}$ is the wave vector, and we use units $\hbar=c=1$), whereas $\mathbf{\hat S}$ is the spin-1 operator given by $3\times 3$ matrices $(\hat{S}_a)_{ij}=-i\epsilon_{aij}$ ($\epsilon_{aij}$ is the Levi-Civita symbol) that act on the Cartesian components of the wave electric field. Canonical orbital AM (OAM) and spin AM (SAM) operators, $\mathbf{\hat L}$ and $\mathbf{\hat S}$, satisfy $so(3)$ algebra and generate rotations in spatial and polarization degrees of freedom, respectively. However, “*the separation of the total AM into orbital and spin parts has restricted physical meaning. ... States with definite values of OAM and SAM do not satisfy the condition of transversality in the general case.*” [@AB]. In 1994, Van Enk and Nienhuis put forward an alternative, non-canonical AM separation, where the modified spin and orbital parts are measurable and consistent with the transversality of the wave, although they are not generators of rotations [@EN].

In classical optics, the two parts of Eq. (\[eqn:1\]) can be unambiguously associated with the OAM and SAM for *paraxial* light, where the eigenmodes of $\hat{L}_z=-i\partial_{\phi}$ ($\phi$ is the azimuthal angle in ${\bf k}$ space) and $\hat{S}_z$ are circularly polarized vortex beams with the corresponding quantum numbers $\ell = 0,\pm 1,\pm 2,...$ 