Goos-H\"anchen Shift and Photonic Spin Hall Effect in Semi-Dirac Material Heterostructures

We investigate the photonic spin Hall effect (PSHE) and the Goos-H\"anchen shift (GH shift) in semi-Dirac materials. Through theoretical modeling, we demonstrate that the anisotropic dielectric function in semi-Dirac materials play a critical role in determining the magnitude and polarity of these optical displacements. Further more, by utilizing the unidirectional drift of massless Dirac electrons in Semi-Dirac materials, we systematically reveal how the drift velocity and direction modulate the behavior of optical displacements. The results indicate that semi-Dirac materials provide a versatile platform for controlling spin-dependent photonic phenomena with their material anisotropy and carrier transport. This work opens a new avenue for designing advanced photonic devices with tunable optical responses, particularly with significant application potential in quantum information processing and topological photonics.