Editing Geometric phase (section)

=== Polarized light in an optical fiber ===
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A second example is linearly polarized light entering a [[single-mode optical fiber]]. Suppose the fiber traces out some path in space, and the light exits the fiber in the same direction as it entered. Then compare the initial and final polarizations. In semiclassical approximation the fiber functions as a [[waveguide]], and the momentum of the light is at all times tangent to the fiber. The polarization can be thought of as an orientation perpendicular to the momentum. As the fiber traces out its path, the momentum vector of the light traces out a path on the sphere in [[momentum space]]. The path is closed, since initial and final directions of the light coincide, and the polarization is a vector tangent to the sphere. Going to momentum space is equivalent to taking the [[Gauss map]]. There are no forces that could make the polarization turn, just the constraint to remain tangent to the sphere. Thus the polarization undergoes [[parallel transport]], and the phase shift is given by the enclosed solid angle (times the spin, which in case of light is&nbsp;1).