Spin Hall effect of linearly polarized light passed through a metasurface

The density of the longitudinal component of the spin angular momentum (SAM) vector is calculated for a paraxial vector Gaussian beam with a periodic one-dimensional modulation. For the beam under consideration, the SAM in the initial plane is zero and the polarization is inhomogeneous and linear. When this beam propagates in free space, due to periodic modulation it is effectively divided into two beams with left-handed and right-handed elliptical polarization. That is, in the cross section of the beam, regions with spins of different signs are separated in space, which is a manifestation of the spin Hall effect. This beam can be formed using a metasurface whose transmission periodically depends on one coordinate.