Geometric phase lens

The design of a lens that modulates the geometric phase of an optical beam by manipulating its polarization is presented. To produce such a geometric phase element with a spatially varying phase function, one needs a wave plate with varying orientation. One can use subwavelength grooves to produce form birefringence, but the variation in orientation generally leads to branch points in the groove pattern. These branch points do not affect the phase of the traversing beam directly because the grooves are subwavelength. However, they do produce errors in the groove orientation, which indirectly leads to errors in the geometric phase function that is implemented. A design procedure is provided to compute the groove pattern for such a rotationally symmetric geometric phase element; and, with the aid of a numerical simulation, the effect of the branch points in the groove pattern on its performance is investigated.