Simultaneous weak measurement of angular and spatial Goos-Hänchen and Imbert-Fedorov shifts

Abstract

We propose and demonstrate the weak measurement scheme to simultaneously measure the amplified angular and spatial contributions to the Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts, due to transmission through a glass plate. We have studied two cases of post-selection using a polarizer in the first case and a quarter-wave plate (QWP)-polarizer combination in the second case. The two cases are analyzed theoretically using Jones calculus of polarization formalism and the results are verified experimentally. In the first case of post-selection, the projection of the polarizer at Δ away from the crossed position amplifies the angular GH and IF shifts, while in the second case of post-selection, the projection of QWP at ±Δ and polarizer kept fixed measures the polarization ellipticity in the beam and thus amplifies the spatial shift along with the angular shift simultaneously, for Δ ≪ 1.