Optical weak measurements without removing the Goos–Hänchen phase

Abstract

Optical weak measurements are a powerful tool for measuring small shifts of optical paths. When applied to the measurement of the Goos–Hänchen shift, in particular, a special step must be added to its protocol: the removal of the relative Goos-Hänchen phase, since its presence generates a destructive influence on the measurement. There is, however, a lack of description in the literature of the precise effect of the Goos–Hänchen phase on weak measurements. In this paper we address this issue, developing an analytic study for a Gaussian beam transmitted through a dielectric structure. We obtain analytic expressions for weak measurements as a function of the relative Goos–Hänchen phase and show how to remove it without the aid of waveplates.