In media with strong spatial dispersion the electric displacement vector andthe electric field are typically linked by a partial differential equation inthe bulk region. The objective of this work is to highlight that in thevicinity of an interface the relation between the macroscopic fields cannot beunivocally determined from the bulk response of the involved materials, butrequires instead the knowledge of internal degrees of freedom of the materials.We derive such relation for the particular case of "wire media", and describe anumerical formalism that enables characterizing the electromagnetic response ofarbitrarily shaped spatially dispersive bodies formed by arrays of crossedwires. The possibility of concentrating the electromagnetic field in a narrowspot by tapering a metamaterial waveguide is discussed.
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