Optical weak measurements without removing the Goos-Haenchen phase

TL;DR

This paper analyzes the impact of the Goos-Haenchen phase on optical weak measurements of small shifts and presents a method to remove this phase analytically without using waveplates.

Contribution

It provides an analytic study of the Goos-Haenchen phase effect on weak measurements and introduces a way to eliminate it without additional optical components.

Findings

Derived analytic expressions for weak measurements considering the Goos-Haenchen phase

Demonstrated removal of the phase without waveplates

Enhanced accuracy in measuring optical path shifts

Abstract

Optical weak measurements are a powerful tool for measuring small shifts of optical paths. When applied to the measurement of the Goos-Haenchen shift, in particular, a special step must be added to its protocol: the removal of the relative Goos-Haenchen 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-Haenchen 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-Haenchen phase and show how to remove it without the aid of waveplates.