Engineering the dielectric function of plasmonic lattices.

We have systematically measured epsilon(omega) of subwavelength aperture arrays fabricated in metal films as a function of aperture size and incidence angle using terahertz time-domain spectroscopy. This approach simultaneously yields both the real and imaginary epsilon(omega) components, enabling deeper insight into the underlying mechanism of the 'enhanced optical transmission' (EOT) phenomenon. For random aperture arrays we find that epsilon(omega) has a plasma response, with an effective plasma frequency that is determined by the waveguide mode cutoff frequency of the individual apertures. However epsilon(omega) in plasmonic lattices is strongly modulated at discrete resonant frequencies that correspond to the reciprocal vectors in the structure factor that are superposed on the plasma envelope response and appear as dips in the EOT spectrum. The existence of a sum rule for the discrete resonance oscillator strengths when the aperture size or incidence angle are changed validates our approach and allows for engineering of the individual resonances in the EOT spectrum.