An Extension of Weak-Value Theory for Birefringence-Induced Displacement Measurements

TL;DR

This paper extends weak-value theory to birefringence-induced displacement measurements, modeling tilt sensitivity in optical devices and validating findings with laboratory experiments, revealing new amplification configurations and sensitivities.

Contribution

It introduces an extended weak-value model for birefringence effects, demonstrating alternative amplification angles and validating these with experimental data.

Findings

Weak-value amplification occurs at new angles beyond previous reports.

Beam divergence enables inverse weak-value amplification configurations.

Maximum measured tilt sensitivity was ~0.58 m/rad, significantly higher than without amplification.

Abstract

We present an investigation into the tilt sensitivity of the canonical, optical, weak-value amplification device (COWVAD), introduced by Duck, Stevenson, and Sudarshan in 1989, for potential application in a Coriolis vibratory gyroscope (CVG). We model the breakdown of the weak-value amplification effect in this device with respect to angle of incidence between the laser beam and the surface of the birefringent crystal. Additionally, we model the effect of beam divergence due to misalignment of the crystals optic axis. We found that the presence of beam divergence allows the architecture to be placed in an inverse weak-value amplification configuration. We found that weak-value amplification occurs at angles other than those reported in Duck 1989. We also present laboratory measurements that support the validity of the mathematical model. The maximum tilt sensitivity measured was ~.58 m/rad, which, while 390 times greater than it would be without weak-value amplification, does not represent the maximum possible sensitivity of the device through weak-value amplification.