Advances in isotropic split ring metamaterials

Abstract — The problem of developing negative µ and negative refraction (NRI) 3D isotropic split ring metamaterials is addressed. First of all the necessary symmetries required to guar-antee an isotropic behavior are analyzed. Secondly an homogenization procedure taking into account spatial dispersion is developed for magnetic split ring metamaterials. It is shown that this homogenization also accounts for all kind of waves (electromagnetic and magnetoinductive) previously reported in negative-µ split ring metamaterials. Finally, the possibility of developing isotropic NRI metamaterials from chiral split ring resonators (SRRs) is discussed in detail In spite of many efforts in this direction (see e.g. [1], [2], [3]) the depelopment of practical 3D isotropic metamaterials is still a challenging issue. This issue will be addressed during the presentation, starting from the generalization of the well known split ring resonator (SRR) configuration. Cubic arrangements of such elements will be considered, and the necessary spatial symetries that guarantee an isotropic behavior in three dimensions will be discussed. From this analysis some proposals to develop periodic and isotropic negative-µ split ring metamaterials will come out [4], [5]. Once the spatial symmetries necessary to ensure electromagnetic isotropy have been identified, the homogenization problem is addressed. Two main kond of waves have been reported in 3D split ring metamaterials: electromagnetic and magnetoinductive [?]. Th