Numerical demonstration of a three-dimensional negative-index metamaterial at optical frequencies.

As a consequent work of the two-dimensional (2D) dendritic metamaterial which has been systematically studied in our previous work, a model of three-dimensional (3D) sphere-rod shaped structure is presented. Based on Drude model of the dielectric function of silver in the visible region, the parametric curves of electromagnetic response to the incident fields have been retrieved from detailed simulations. It is shown that the simultaneously negative values of permittivity and permeability in the optical range lead to a negative refractive index (NIM) through adjusting structural parameters, only the dimensions of the unit cells satisfy the effective medium theory. We therefore conclude that the proposed model offers a feasible route to fabricating 3D optical NIMs by 'bottom-up' approach.