On the deviation of metamaterial spheres from effective medium

Abstract

We analyse the convergence of the actual properties of finite subwavelength metamaterial samples where all the prerequisites for a reliable effective medium description, except for the finite size, are fulfilled, towards the effective medium predictions. We show that the convergence is rather slow and it is likely that hundreds of thousands of individual meta-atoms must be assembled together before the properties of the resulting structure can be claimed to correspond to those a bulk material. These observations are directly relevant for practical design of metamaterials and their future development.