Flat polarization-controlled cylindrical lens based on the Pancharatnam–Berry geometric phase

Abstract

The working principle of ordinary refractive lenses can be explained in terms\nof the space-variant optical phase retardations they introduce, which reshape\nthe optical wavefront curvature and hence affect the subsequent light\npropagation. These phases, in turn, are due to the varying optical path length\nseen by light at different transverse positions relative to the lens centre. A\nsimilar lensing behavior can however be obtained when the optical phases are\nintroduced by an entirely different mechanism. Here, we consider the "geometric\nphases" that arise from the polarization transformations occurring in\nanisotropic optical media, named after Pancharatnam and Berry. The medium\nanisotropy axis is taken to be space-variant in the transverse plane and the\nresulting varying geometric phases give rise to the wavefront reshaping and\nlensing effect, which however depends also on the input polarization. We\ndescribe the realization and characterization of a cylindrical geometric-phase\nlens that is converging for a given input circular polarization state and\ndiverging for the orthogonal one, which provides one of the simplest possible\nexamples of optical element based on geometric phases. The demonstrated lens is\nflat and only few microns thick (not including the supporting substrates);\nmoreover, its working wavelength can be tuned and the lensing can be switched\non and off by the action of an external control electric field. Other kinds of\nlenses or more general phase elements inducing different wavefront distortions\ncan be obtained by a similar approach. Besides their potential for\noptoelectronic technology, these devices offer good opportunities for\nintroducing college-level students to an advanced topic of modern physics, such\nas the Berry phase, with the help of interesting optical demonstrations.\n