Statistical analysis of affect of parameter variations on double-negative behavior of metamaterials

Non-metallic double-negative (DNG) metamaterials can be formed by three-dimensional (3D) periodic arrays of non-metallic spheres. Since such metamaterials usually show DNG behavior in the neighborhood of the Mie resonances of the spheres, even small variations in their geometric and electromagnetic material parameters affect their DNG behavior significantly. Practically, all fabrications induce these variations in the form of tolerances. This paper presents a statistics-based analysis of the affect of fabrication tolerances on the effective constitutive parameters and DNG bandwidths of non-metallic metamaterials. Results show that even 3% variation in the geometric and electromagnetic material parameters may extinguish the DNG behavior of a non-metallic metamaterial.