Shift vector as the geometric origin of beam shifts

Abstract

Goos-H\"anchen (GH) and Imbert-Fedorov (IF) shifts are lateral and transverse displacements of a wave packet reflecting off a surface. A dramatic real-space manifestation of wave-packet phases, they have traditionally been analyzed in a model-dependent fashion. Here, we argue that GH and IF shifts admit a general geometrical description and arise from a gauge invariant geometric phase. In particular, we show GH/IF shifts can be naturally captured by a shift vector, analogous to the shift vector from shift currents in the bulk photovoltaic effect. Employing Wilson loops to visualize the scattering processes contributing to the shift vector, we separate the shift into an intrinsic (depends solely on the system bulk) and an extrinsic part. This enables us to establish a clear model-independent link between symmetry and the presence/absence of intrinsic and extrinsic GH/IF shifts.