k-dependent optics of nanostructures: Spatial dispersion of metallic nanorings and split-ring resonators

The response of matter on an electromagnetic wave at a certain point and time depends on the field strength prior to this time and at places close to this point. Hence the material parameters are functions of the frequency. and the wave vector (k) over right arrow, in general. While the temporal dispersion is common knowledge, spatial dispersion in usually disregarded. However it becomes crucial in the optical response of nanostructures. Here we map the complete (k) over right arrow -dependent optical response of a split-ring-resonator array over a broad frequency range via Mueller-matrix spectroscopic ellipsometry at different angles of incidence and all azimuthal orientations. The comparison with a closed-ring structure elucidates the rule of spatial dispersion in metal-dielectric nanostructures.