Fiber optics in curved space-times
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.