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.
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