Determining the twist in an optical fiber

Abstract

We determine the twist in a birefringent optical fiber from measurements, at one end of the fiber, of the fiber response to an impulsive source at the same end. This is the inverse problem of determining a non-constant coefficient, of a first order hyperbolic system in one space dimension with two speeds of propagation, from measurements at one end of an interval, of the solution of this system corresponding to an impulsive source at the same end. We prove a stability result for this inverse problem and give a provable reconstruction algorithm for this inverse problem.