Fundamental limitations of Huygens metasurfaces for optical beam shaping

Optical dielectric metasurfaces composed of arrayed nanostructures are expected to enable arbitrary spatial control of incident wavefronts with subwavelength spatial resolution. For phase modulation, one often resorts to two physical effects to implement a 2\pi-phase excursion. The first effect relies on guidance by tall nanoscale pillars and the second one exploits resonant confinement by nanoresonators with two degenerate Mie-resonances. The first approach requires high aspect ratios, while the second one, known as Huygens metasurfaces, is much flatter, and thus easier to manufacture. We compare the two approaches, more focusing on conceptual rather than technological issues, and identify fundamental limitations with the latter. We explain the origin of the limitations based on general arguments, such as reciprocity, multimode/monomode operation and symmetry breaking.