Geometric spin Hall effect and polarization-dependent transformations in the oblique section of a paraxial light beam

Abstract

The spatial structure of light beams is usually considered in the transverse cross sections but supplementary analysis of the field pattern across an oblique plane may disclose additional details of the internal beam structure and energy flow distributions. Their manifestations are known as ‘geometric spin Hall effect of light’ (gSHEL). We analyze the ‘practical’ gSHEL scheme in which the light energy distribution is registered by a detector whose input plane is inclined with respect to the propagation axis. Based on the vector beam model and using the formalism of optical Wigner matrices, we find that the oblique-plane energy distribution differs from that observed in the transverse cross section. This difference is associated with the azimuthal energy circulation and the orbital angular momentum (AM) of the beam; it can be expressed as the lateral shift of the mean-weighted beam position (beam centroid). The similar effect can be observed in elliptically polarized beams without orbital AM: there, the oblique-section projection reveals a specific asymmetry induced by the spin AM in the longitudinal field components of such beams. The polarization-induced oblique-section beam shift is rather weak in paraxial approximation but can be observable if the light-detecting procedure is selectively sensitive to the longitudinal optical-field component.