We demonstrate that the presence of a supporting substrate can break the symmetry of a metamaterial structure, changing the symmetry of its effective parameters, and giving rise to bianisotropy. This indicates that magneto-electric coupling will occur in all metamaterials fabricated on a substrate, including those with symmetric designs.
@article{arxiv.1006.1159,
title = {Substrate-induced bianisotropy in metamaterials},
author = {David A. Powell and Yuri S. Kivshar},
journal= {arXiv preprint arXiv:1006.1159},
year = {2015}
}