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The polarization state of a light beam is related to its spin angular momentum and can be represented on the Poincaré sphere. We propose a sphere for light beams in analogous orbital angular momentum states. Using the Poincaré-sphere equivalent, we interpret the rotational frequency shift for light beams with orbital angular momentum Phys. Rev. Lett. 80, 3217 (1998) as a dynamically evolving geometric phase.
Padgett et al. (Thu,) studied this question.