Role of in-plane shift in reconstructing the photonic spin Hall effect

The photonic spin Hall effect (SHE) manifests itself as in-plane and transverse spin-dependent shifts of left- and right-handed circularly polarized (LCP, RCP) components and originates from the spin-orbit interaction (SOI) of light, where extrinsic orbital angular momentum (EOAM) can induce these shifts. However, previous studies mainly focus on the SOI corresponding to transverse shifts and generally consider the paraxial approximation case. In this Letter, we reconstruct a more general theory of the photonic SHE in the non-paraxial case and reveal that the induction of an in-plane shift mainly relies on the EOAM of the y direction, supplemented by the EOAM of the x and z directions under the laboratory coordinate system. In addition, the EOAM in the x and z directions completely determine the transverse shift. Moreover, the angular momentum conversion between the LCP and RCP components results in the angular momentum of the LCP (RCP) component of the incident Gaussian beam not being equal to the sum of the angular momentum of the LCP (RCP) component of the reflected and transmitted light. These findings explore the influence of in-plane shifts on the SOI of light and provide an in-depth understanding of the photonic SHE.