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 nanorod meta-atoms of several geometries, which included cylinders, triangles, squares, hexagons, octagons, and truncated cones. By analyzing light propagation through these meta-atoms for three different wavelengths (632.8, 545, and 50 nm), 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-sectional area of meta-atoms. These meta-atom optical properties are independent of its shape if its geometry has a C3 or larger rotational symmetry. This optical invariance has significant implications for the topological optimization of flat optics.