A Generalized Sagnac-Wang-Fizeau formula

TL;DR

This paper provides a relativistic analysis of deformable interferometers, unifying Sagnac, Wang, and Fizeau effects, and offers explicit formulas for phase shifts including optical path stretching.

Contribution

It introduces a comprehensive relativistic framework that unifies multiple interferometric effects and rigorously proves Wang's empirical formula.

Findings

Derives explicit first-order formulas for phase shifts in deformable interferometers.

Unifies Sagnac, Wang, and Fizeau effects within a single relativistic scheme.

Provides a rigorous proof of Wang's empirical formula.

Abstract

We present a special-relativistic analysis of deformable interferometers where counter propagating beams share a common optical path. The optical path is allowed to change rather arbitrarily and need not be stationary. We show that, in the absence of dispersion the phase shift has two contributions. To leading order in $v/c$ one contribution is given by Wang empirical formula for deformable Sagnac interferometers. The second contribution is due to the stretching of the optical path and we give an explicit formula for this stretch term valid to first order in $v/c$. The analysis provides a unifying framework incorporating the Sagnac, Wang and Fizeau effects in a single scheme and gives a rigorous proof of Wang empirical formula.