Twisted Electromagnetic Modes and Sagnac Ring-Lasers

TL;DR

This paper develops a new approximation method to analyze twisted electromagnetic modes in rotating ring-lasers, revealing how the cavity's geometry influences the Sagnac frequency and aiding in measurements of Earth's gravito-magnetic effects.

Contribution

It introduces a novel approximation scheme for solving Maxwell's equations in rotating cavities, linking cavity geometry to electromagnetic mode spectra and Sagnac frequency shifts.

Findings

Existence of TE and TM modes in rotating cavities under certain conditions

Mode spectrum depends on the cavity's Frenet torsion

Potential implications for measuring Earth's gravito-magnetic effects

Abstract

A new approximation scheme, designed to solve the covariant Maxwell equations inside a rotating hollow slender conducting cavity (modelling a ring-laser), is constructed. It is shown that for well-defined conditions there exist TE and TM modes with respect to the longitudinal axis of the cavity. A twisted mode spectrum is found to depend on the integrated Frenet torsion of the cavity and this in turn may affect the Sagnac beat frequency induced by a non-zero rotation of the cavity. The analysis is motivated by attempts to use ring-lasers to measure terrestrial gravito-magnetism or the Lense-Thirring effect produced by the rotation of the Earth.