Mesoscopic effects in discretised metamaterial spheres

It is well known that effective medium description of metamaterials requires much caution, even for strongly subwavelength systems. Boundary effects play a dramatic role in finite samples with discrete structure, making their observable properties quite different from the predictions of effective medium theory. We report some new findings regarding the distinction between a homogenised response and actual properties of discrete structures, looking into canonical shape of metamaterial objects. Even for large size (up to 20000 “meta-atoms”), we observe a difference between large discretised spheres and a continuous one, which is important for practical design and future development of metamaterials. Finally, we also provide the results for non-resonant discrete finite systems