Proposed isotropic negative index in three-dimensional optical metamaterials

A simple route toward achieving an isotropic optical negative index in three dimensions is theoretically proposed. We show that, in contrast with previous studies, the plasmonic ring resonators, symmetrically split with an odd number of gaps, have both degenerate electric and magnetic resonances and thus provide an isotropic negative index if randomly distributed in a host medium. For an even number of gaps, the electric and magnetic dipoles sufficiently overlap only by additional symmetry breaking, which is demonstrated to allow unique control of the relative contribution from higher-order multipolar moments.