GEOMETRIC PHASES FROM STACKS OF CRYSTAL PLATES

With twisted stacks of N polarizers P or retarders R, the polarization of a light beam can be cycled around the Poincare sphere on N similar arcs of great P or small R circles. We calculate the phase changes ar ound these cycles (geometric for P; geometric + dynamical for R). In t he continuum limit N -->infinity of a smoothly twisting medium, a P st ack forces the light to follow its changing polarization, and the phas e is the solid angle of the associated loop on the sphere; for an R st ack, on the other hand, it is only in the adiabatic limit of slow twis t (where the dynamical phase is large) that the geometric phase corres ponds to that of the loop specified by the changing eigenpolarization of the medium. The predicted phase shifts are observed as fringe shift s in an interferometer for N = 2, 3 and 4.