Unveiling invariant optical properties of dielectric meta-atoms

The phase-shift, transmittance, and polarization properties of meta-atoms are investigated, motivated by their use as building blocks of metasurfaces used in metalenses, holograms, and beam shaping. We studied dielectric rod meta-atoms of several geometries, which included: cylinders, squares, polygons, and truncated cones. By analyzing light propagation through these meta-atoms, we show that the phase-shift introduced is independent of their cross-section shape, contrary to the expected behavior. Additionally, we show that the polarization response is independent of the shape, and that the transmittance is partially shape independent. We identify a novel dependence of phase-shift on the effective cross-section area of meta-atoms. These meta-atom transmission properties are independent of its shape if its geometry has C3 or larger rotational symmetry. This optical invariance has significant implications in the topological optimization of flat optics.