Generalized Brillouin diagrams for evanescent waves in metamaterials with interelement coupling

A graphical representation for two-dimensional periodic structures is introduced that provides the full information contained in the dispersion equation: not only for the pass band but for the neighboring stop bands as well. It is a seamless natural extension of Brillouin diagrams obtained by adding eight new zones which incorporate the properties of evanescent waves. The accuracy of the infinite lattice approximation is tested both by simulations and experiments using magnetoinductive waves. For waves propagating in one direction and evanescent in the other direction, the results of the three different methods are shown to be in good agreement. The versatility of the new representation and its applicability to the design of near-field manipulating metamaterials is discussed.