Revisiting the wire medium: a resonant metalens

Abstract: This article is the first one in a series of two dealing with the concept of "resonant metalens" we recently introduced [Phys. Rev. Lett. 104, 203901 (2010)]. Here, we focus on the physics of a medium with finite dimensions consisting on a square lattice of parallel conducting wires arranged on a sub-wavelength scale. This medium supports electromagnetic fields that vary much faster than the operating wavelength. We show that such modes are dispersive due to the finiteness of the medium. Their dispersion relation is established in a simple way, a link with designer plasmons is made, and the canalization phenomenon is reinterpreted at the light of our model. We explain how to take advantage of this dispersion in order to code sub-wavelength wave fields in time. Finally, we show that the resonant nature of the medium ensures an efficient coupling of these modes with free space propagating waves and, thanks to the Purcell effect, with a source placed in the near field of the medium.