In this paper, we develop a finite-difference frequency-domain (FDFD) based formalism to model spatially dispersive metamaterials formed by two nonconnected arrays of parallel wires (“double-wire medium”). While generally, in order to characterize the effective response of arbitrarily shaped regions formed by the double wire medium, electromagnetic simulators would need to take into account all the minute details of the microstructure, here we demonstrate that it is possible to numerically model such materials by discretizing the macroscopic Maxwell’s equations taking into account the effects of spatial dispersion [1, 2]. The proposed formalism enables modeling complex-shaped metamaterial structures in a straightforward manner that otherwise would require intensive computational efforts. As an application, we study the collimating properties of an ultradense array of crossed metallic wires. Using our FDFD approach we confirm that such substrate supports strongly confined guided modes and that a planar slab of the structured material makes a superlens that can restore the subwavelength details of the source [3].

References

[1] M. G. Silveirinha, C. A. Fernandes, IEEE Trans. on Microwave Theory and Tech., 52 , 889, (2004).
[2] C. R. Simovski, and P. A. Belov, Phys. Rev. E, 70, 046616 (2004).
[3] M. G. Silveirinha et. al., Phys. Rev. B. 78, 195121 (2008).