Design of continuously variant metasurfaces for conformal transformation optics

Metasurfaces optics and structured light represent two emerging paradigms which are revolutionizing optics in a wide range of fields, from imaging to telecommunications, both in the classical and single-photon regimes. In this work, we present and describe a method for the design of high-resolution geometric-phase metasurfaces in the form of continuously variant sub-wavelength gratings, and we demonstrate how this technique is suitable for harmonic phase masks implementing conformal optical transformations. In this framework, we revisit the metasurface design of blazed gratings and spiral phase plates, the so-called q-plates, and we extend the method to the metasurface implementation of two conformal mappings, the log-pol and the circular-sector transformation, which have been exploited successfully to perform the generation, sorting and manipulation of structured light beams carrying orbital angular momentum.