Realization of doubly inhomogeneous waveplates for structuring of light beams

Waveplates having spatially varying fast-axis orientation and retardance provide an elegant and easy way to locally manipulate different attributes of light beams, namely, polarization, amplitude, and phase, leading to the generation of exotic structured light beams. The fabrication of such doubly inhomogeneous waveplates (d-plates) is more complex, compared with that of singly inhomogeneous waveplates (s-plates) having uniform retardance, which can be easily fabricated by different means such as photoalignment of liquid crystals, metasurfaces, etc. Here, exploiting the SU(2) formalism, we establish analytically that any d-plate can be equivalently implemented using a pair of quarter-wave s-plates and a half-wave s-plate. To underline the scope of this method, we propose novel d-plates toward complex amplitude shaping and also for imparting a polarization-dependent phase profile to a scalar light beam. For these two illustrations, the corresponding three-s-plate gadget is constructed, and its functioning is validated with extensive numerical simulations. The main result and its illustrations are generic and agnostic to the way the s-plates are fabricated, and we believe they carry the potential to push the current state of the art in interdisciplinary applications involving structured light beams.