# Gauge-field description of Sagnac frequency shift and mode hybridization in a rotating cavity

## TL;DR

This paper models a rotating optical cavity using gauge fields, revealing how rotation induces Sagnac frequency shifts and mode hybridization, with potential applications in measuring rotation through far-field analysis.

## Contribution

It introduces a gauge-field framework to describe Sagnac shifts and mode hybridization in rotating cavities, supported by analytical derivations and finite element simulations.

## Key findings

- Rotation induces a synthetic gauge field in the cavity.
- Hybridization of CW and CCW modes depends on rotation.
- Far-field variations can be used to measure rotation.

## Abstract

Active optical systems can give rise to intriguing phenomena and applications that are not available in conventional passive systems. Structural rotation has been widely employed to achieve non-reciprocity or time-reversal symmetry breaking. Here, we examine the quasi-normal modes and scattering properties of a two-dimensional cylindrical cavity under rotation. In addition to the familiar phenomenon of Sagnac frequency shift, we observe the the hybridization of the clockwise(CW) and counter-clockwise(CCW) chiral modes of the cavity controlled by the rotation. The rotation tends to suppress one chiral mode while amplify the other, and it leads to the variation of the far field. The phenomenon can be understood as the result of a synthetic gauge field induced by the rotation of the cylinder. We explicitly derived this gauge field and the resulting Sagnac frequency shift. The analytical results are corroborated by finite element simulations. Our results can be applied in the measurement of rotating devices by probing the far field.