A generalized additional boundary condition for mushroom-type and bed-of-nails-type wire media

Abstract—An additional boundary condition (ABC) for mush-room 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 gener-alization is presented based on charge conservation. The new ABC leads to results that are in good agreement with full-wave simulations. Index Terms—Boundary conditions, composite material struc-tures, electromagnetic (EM) analysis, EM modeling, nanostruc-tures. I