Synthesis of universal space-variant polarization gadgets

The synthesis of a single gadget from elementary polarization optical elements, such as a cascade of waveplates, to realize any and every polarization transformation has been well known for over thirty years. However, the two-dimensional equivalent, where each transverse location or pixel is separately capable of producing any polarization transformation in an ideally reprogrammable fashion, has only recently been developed. This mini-review covers the progress over the past decade in synthesizing such gadgets that perform general spatially varying polarization transformations. Particularly, we will discuss their implementation and recent experimental demonstrations on three platforms: dielectric metasurfaces, liquid crystal (LC) metasurfaces, and liquid crystal on silicon (LCoS) displays.