Disorder-immune metasurfaces with constituents exhibiting the anapole mode

Common optical metasurfaces are two-dimensional functional devices composed of periodically arranged subwavelength constituents. Here, we achieved the positional-disorder-immune metasurfaces composed of core-shell cylinders which successively exhibit the magnetic dipole (MD) resonant, non-radiating anapole, and electric dipole (ED) resonant modes when their outer radii are fixed and the inner radii change continuously in a range. The performances of the metasurfaces under a periodically structural design are not degraded even when the positions of the cylinders are subjected to random and considerable displacements. The positional-disorder-immunity is due to the weak non-local effect of the metasurfaces. Because the multiple scattering among cylinders is weak and insensitive to the spacing among the cylinders around the ED and MD resonant modes and vanishing irrespective of the spacing at the non-radiating anapole mode, the reflection properties including the reflection phase and reflectivity of the metasurfaces are insensitive to the spacing between neighboring cylinders for this entire variation range of the inner radius. Our findings can have important implications in understanding the underlying mechanism of the positional-disorder-immunity and provide a unique approach to achieve metasurfaces with various performances robust against large positional disorders. We expect the present work to open a door for the various applications of the metasurfaces in some harsh and unstable environments.