Non-local susceptibility for a bounded homogenized wire medium in the spatial domain

Here, we present different formulations for wave interaction problems of bounded homogenized wire media in the spatial domain. We demonstrate that two previous methods based on the wave expansion and transport equation are equivalent to each other, and to a charge carrier model involving particle reflection at the boundary. The role of a virtual interface is discussed, and it is found to be analogous to that for natural excitonic materials. An important observation is that the non-local susceptibility x(r, r') for a non-translationally invariant homogenized wire medium is represented by a Green's function in the spatial domain subject to boundary conditions at the material boundaries.