Engineered photonic spin Hall effect of Gaussian beam in antisymmetric parity-time metamaterials

A model of the photonic spin Hall effect (PSHE) in antisymmetric parity-time (APT) metamaterials with incidence of Gaussian beams is proposed here. We derive the displacement expression of the PSHE in APT metamaterials based on the transport properties of Gaussian beams in positive and negative refractive index materials. Furthermore, detailed discussions are provided on the APT scattering matrix, eigenstate ratio, and response near exceptional points in the case of loss or gain. In contrast to the unidirectional non-reflection in parity-time (PT) symmetric systems, the transverse shift that arises from both sides of the APT structure is consistent. By effectively adjusting the parameters of APT materials, we achieve giant displacements of the transverse shift. Finally, we present a multi-layer APT structure consisting of alternating left-handed and right-handed materials. By increasing the number of layers, Bragg oscillations can be generated, leading to an increase in resonant peaks in transverse shift. This study presents a new approach to achieving giant transverse shifts in the APT structure. This lays a theoretical foundation for the fabrication of related nano-optical devices.