Connection between extraordinary transmission and negative refraction in a prism of stacked sub-wavelength hole arrays

A prism engineered by stacking sub-wavelength hole arrays is shown as a route to negative refraction in any frequency range. We analyse numerically and experimentally at the near field zone, several propagation regimes and bands with orthogonal polarizations, and find that negative refraction is intimately linked to the extraordinary transmission resonance of sub-wavelength hole arrays. Negative indices of refraction start from near to zero values for the lower mode while for the second one they are positive. The p-polarization component has a positive refractive index within both bands. The way to engineering negative refraction devices in any region of the spectrum is open.