An alternative calculation of the Casimir forces between birefringent plates

TL;DR

This paper verifies the Casimir forces and torque between birefringent plates using an alternative method, confirming previous results and highlighting the potential for experimental measurement of the torque.

Contribution

It provides an independent calculation of Casimir forces and torque between birefringent plates by using the electromagnetic stress tensor, validating earlier Helmholtz free energy results.

Findings

Confirmed the Casimir force results with an alternative method

Identified the existence of a Casimir torque aligning optical axes

Supported potential experimental measurement of the torque

Abstract

Barash has calculated the Casimir forces between parallel birefringent plates with optical axes parallel to the plate boundaries [Izv. Vyssh. Uchebn.\ Zaved., Radiofiz., {\bf 12}, 1637 (1978)]. The interesting new feature of the solution compared to the case of isotropic plates is the existence of a Casimir torque which acts to line up the optical axes if they are not parallel or perpendicular. The forces were found from a calculation of the Helmholtz free energy of the electromagnetic field. Given the length of the calculations in this problem and hopes of an experimental measurement of the torque, it is important to check the results for the Casimir forces by a different method. We provide this check by calculating the electromagnetic stress tensor between the plates and showing that the resulting forces are in agreement with those found by Barash.