Designing Collective Non-local Responses of Metasurfaces

We propose a numerically efficient `adjoint' inverse design method to optimize a planar structure of dipole scatterers, to manipulate the radiation from an electric dipole emitter. Several examples are presented: modification of the near-field to provide a 3 fold enhancement in power emission; re-structuring the far-field radiation pattern to exhibit chosen directivity; and the design of a discrete `Luneburg lens'. Additionally, we develop a clear physical interpretation of the optimized structure, by extracting `eigen-polarizabilities' of the system. We find that large `eigen-polarizability' corresponds to a large collective response of the scatterers. This framework may find utility in wavefront shaping as well as in the design and characterisation of non-local metasurfaces.