Geometric phases in optics: Polarization of light propagating in helical optical fibers

The optical geometric phase (OGP) is directly associated with the polarization of light. We investigate the physical principles underlying the occurrence of the OGP for a single-mode light beam propagating in a single-mode optical fiber wound into a circular helix configuration, with and without stress-induced birefringence. The effects of the curvature and torsion of the helical fiber on the rotation of the polarization vector and the associated OGP are discussed. Analytic expressions are derived for the polarization vector and Stokes parameters for any initial polarization state of the light entering the helical fiber, as well as for the OGP of the light as a function of helix arclength. Additionally, the intensity of a superposition of the initial and final beams, which depends on the final OGP, is derived. Furthermore, the relationship between the OGP and the solid angle subtended by the tangent vector of the helix plotted on the Poincar\'e sphere is analyzed and the effects of fluctuations of the parameters specifying the geometry and the material characteristics of the helical fiber on the OGP are considered. We also point out that the OGP is a geometric phase and not a topological phase and therefore is not topologically protected against local perturbations which can adversely affect fault tolerance.