  The Parachatnam-Berry phase (PBP) is a geometric phase associated with the
polarization of light propagating in optical systems. Here, we investigate the
physical principles underlying the occurrence of PBP for a single-mode light
beam propagating in a single-mode optical fiber with no significant
stress-induced birefringence wound into a circular helix configuration. We
discuss the effects of curvature and torsion of the helical fiber on the
rotation of the polarization vector and the associated PBP. We find the
analytic solution for the polarization vector and Stokes parameters of the
light for any initial polarization state of the light entering the helical
fiber, the analytic expression for the PBP of the light for periodic transport
of the light, the intensity of a superposition of the initial and final beams
which depends on the PBP, and we discuss the effects of fluctuations of the
parameters specifying the geometry and the material characteristics of the
helical fiber on the PBP. We also discuss the relationship between the PBP and
the solid angle subtended by the tangent vector of the helix plotted on the
unit sphere.
