Differential interference theory of vortex beam at interface reflection

Weak measurement technique based on weak-value amplification offers an effective method to detect the tiny spin splitting in the photonic spin Hall effect. However, its performance is constrained under conditions of strong coupling or near-orthogonality between the pre- and post-selected states. Based on differential interference theory, this work establishes a relation between the spin-dependent displacement and the amplified displacement for vortex beam with arbitrary topological charge under partial reflection at an air–glass interface. The relation remains valid even under strong-coupling conditions or when the pre- and post-selected states are nearly orthogonal, and is applicable for arbitrary incident linear polarizations. The corresponding characteristics of vortex beam reflected at an air–glass interface is systematically analyzed, and the influences of key parameters including the incident angle, topological charge, incident polarization state, post-selection angle, and propagation distance on the amplified displacement are elucidated. This study provides a valuable theoretical foundation for the applications of vortex beam in precision optical measurement and optical micromanipulation.