The working principle of ordinary refractive lenses can be explained in terms of the space-variant
optical phase retardations they introduce, which reshape the optical wavefront curvature and hence
affect the subsequent light propagation. These phases, in turn, are due to the varying optical path
length followed by light at different transverse positions relative to the lens center. A similar
lensing behavior can, however, be obtained when the optical phases are introduced by an entirely
different mechanism. Here, we consider the ‘geometric phases’ that arise from the polarization
transformations occurring in anisotropic optical media, named after Pancharatnam and Berry. The
medium anisotropy axis is taken to be space-variant in the transverse plane and the resulting
varying geometric phases give rise to the wavefront reshaping and lensing effect, which however
also depends on the input polarization. We describe the realization and characterization of a
cylindrical geometric-pha…