Axial dependence of optical weak measurements in the critical region

TL;DR

This paper investigates the axial dependence of optical weak measurements near the critical angle, focusing on interference effects and the accurate estimation of the Goos-Haenchen shift for different beam parameters and materials.

Contribution

It provides a detailed numerical analysis of the interference between s and p polarized waves near the critical angle, enabling better reproduction of GH curves and guiding experimental setups.

Findings

Frequency crossover observed near the critical angle

Conditions identified to avoid axial deformations in GH measurements

Predicted weak measurement curves for various laser beam sizes and materials

Abstract

The interference between optical beams of different polarizations plays a fundamental role in reproducing the optical analog of the electron spin weak measurement. The extraordinary point in optical weak measurements is represented by the possibility to estimate with great accuracy the Goos-Haenchen (GH) shift by measuring the distance between the peak of the outgoing beams for two opposite rotation angles of the polarizers located before and after the dielectric block. Starting from the numerical calculation of the GH shift, which clearly shows a frequency crossover for incidence near to the critical angle, we present a detailed study of the interference between s and p polarized waves in the critical region. This allows to determine in which conditions it is possible to avoid axial deformations and reproduce the GH curves. In view of a possible experimental implementation, we give the expected weak measurement curves for Gaussian lasers of different beam waist sizes propagating through borosilicate (BK7) and fused silica dielectric blocks.