Design of three-dimensional isotropic negative-refractive-index metamaterials with wideband response based on an effective-medium approach

Negative-refractive-index metamaterials (NRIMs) can provide opportunities for many new applications, but they are difficult to manufacture, especially when forced to work at high frequencies and required to be three-dimensionally isotropic. By integrating an effective-medium approach into all-dielectric left-handed materials (LHMs) and utilizing self-assembly, we developed a method to design three-dimensional NRIMs that can work in high frequencies and are suitable for mass production. The NRIMs are composed of arrays of spheres that are made from artificial media, which are devised under the effective-medium method in advance. Two cases with different close-packed structures were studied for verification purposes. Finite element analysis showed that both cases can achieve negative refraction within 14.5-15.2 GHz (Ku band), which qualifies as wideband. Negative refraction was further confirmed by investigating the resonance mode of units in each model. Dispersion analysis demonstrated isotropism and consistent behaviors in all cases, indicating the robustness of these properties over disorder accompanied by self-assembly. The proposed NRIM model is intrinsically isotropic, three-dimensional, passive, mass-producible, machinable and thus readily applicable.