# Maxwell Eigenmode approach to the Casimir-Lifshitz Torque

## TL;DR

This paper presents a systematic eigenmode-based method to derive the Casimir-Lifshitz torque between birefringent media, extending previous results and enabling analysis of various anisotropic materials.

## Contribution

It introduces a transparent eigenmode decomposition approach that generalizes Barash's calculation to include magnetic birefringence and finite thickness effects.

## Key findings

- Derived a comprehensive formula for Casimir-Lifshitz torque in birefringent media.
- Extended previous results to magnetic and electric birefringence.
- Provides a framework for analyzing anisotropic materials with finite thickness.

## Abstract

More than forty years ago, Barash published a calculation of the full retarded Casimir-Lifshitz torque for planar birefringent media with arbitrary degrees of anisotropy. An independent theoretical confirmation has been lacking since. We report a systematic and transparent derivation of the torque between two media with both electric and magnetic birefringence. Our approach, based on an eigenmode decomposition of Maxwell's equations, generalizes Barash's result for electrically birefringent materials, and can be generalized to a wide range of anisotropic materials and finite thickness effects.