Fiber optics in curved space-times

TL;DR

This paper develops a comprehensive theoretical framework for analyzing electromagnetic modes in arbitrarily bent optical fibers within curved space-times, incorporating gravitational effects and fiber bending phenomena.

Contribution

It introduces a perturbative scheme to solve Maxwell's equations for complex fiber geometries in general stationary space-times, extending previous models beyond ray optics.

Findings

Includes gravitational redshift and Sagnac effect in phase transport equations

Generalizes Rytov's law to curved space-time

Identifies inverse spin Hall effects due to bending and gravity

Abstract

Single-mode fibers are used in fiber-optic gyroscopes to measure the Sagnac effect and are planned to be used in forthcoming experiments on the gravitationally induced phase shift in single photons. However, current theoretical models of such experiments are limited to ray-optics approximations or, if based on wave optics, to a restricted class of fiber alignments. To overcome these shortcomings, this paper develops a comprehensive perturbative scheme to solve for electromagnetic modes, i.e., monochromatic solutions to Maxwell's equations, of arbitrarily bent step-index fibers in general stationary space-times. This leads to transport equations for the electromagnetic phase and polarization that include the gravitational redshift, the Sagnac effect, a generalization of Rytov's law to curved space, a gravitational Faraday effect in the form of shift-induced gyrotropy, as well as inverse spin Hall effects caused by fiber bending, gravitational acceleration, and space-time curvature.