The challenge of homogenization in metamaterials

The problem of homogenization, i.e. substantial reduction of the electrical size of the average lattice constant, of electromagnetic left-handed (LH), or more generally composite right/left-handed (CRLH) metamaterials (MTMs), is presented. The undesirable effects of an electrical very large structural unit cell are explained and illustrated by full-wave simulations and experiments with CRLH mushroom structures. These effects are limited bandwidth, anisotropy, poor refraction due to coupling of the fundamental wave with space harmonics and diffraction at interfaces with other media. Transmission line method (TLM) simulations demonstrate that homogenization may mitigate or suppress these parasitic effects. In addition, the challenging necessity of drastically increasing inductances and capacitances in the homogenization process is demonstrated for CRLH MTMs.