  Polarization vectors of light traveling in a coiled optical fiber rotate
around its propagating axis even in the absence of birefringence. This rotation
was usually explained due to the Pancharatnam-Berry phase of spin-1 photons.
Here, we use a purely geometric method to understand this rotation. We show
that similar geometric rotations also exist for twisted light carrying orbital
angular momentum (OAM). The corresponding geometric phase can be applied in
photonic OAM-state-based quantum computation and quantum sensing.
