Path dependence of the geometric rotation of polarization in optical fibers

The geometric rotation of the polarization angle in a ideal cylindrical optical fiber without birefringence is obtained for arbitrary fiber paths in terms of the image of the path in the tangent vector space. The result extends a recent result of Chiao and Wu [Phys. Rev. Lett. 57, 933 (1986)] restricted to paths with parallel ends, which was derived from Berry's phase in the adiabatic limit of quantum mechanics [Proc. R. Soc. London Ser. A 392,45 (1984)]. The treatment given here is purely classical and uses differential geometry to extend earlier work by Ross [Opt. Quantum Electron. 16, 455 (1984)] on the uniform helix.