A Generalized Additional Boundary Condition for Mushroom-Type and Bed-of-Nails-Type Wire Media

An additional boundary condition (ABC) for mushroom or bed-of-nails metamaterials is generalized for thin 3-D or 2-D material patches or ground planes. It is shown that the usual ABC necessary for the homogenization of these wire-medium metamaterials fails for thin imperfect conductors, and a generalization is presented based on charge conservation. The new ABC leads to results that are in good agreement with full-wave simulations.