Non-local susceptibility of the wire medium in the spatial domain considering material boundaries

We show that the non-local susceptibility (chi) over bar (r, r') for a non-translationally invariant homogenized wire medium is, modulo a constant, given by a simple Green function related to the material geometry. We also show that two previous methods for solving wave interaction problems for bounded wire media (wave expansion method and transport equation) are equivalent to each other, and to a third method involving particle reflection at the boundary. We discuss the importance of the dead layer or virtual interface, and find it to be analogous to the excitonic semiconductor case. Several examples are provided to clarify the material.