Analysis of transmission line meta-materials at optical wavelength

Following the transmission line formalism, we design a metamaterial structure that exhibts negative refraction in the red part of the visible spectrum.The structure is a waveguide consisting of an Al₂O ₃ top layer, 2D array of Au dots, an Al₂O₃ spacer and a Ag ground plane. The Au dot array with period of 250 nm were patterned by an electron beam lithography technique. We confirm experimentally and numerically that threre is a mode shifting to the lower energy side as the wavevector increases. Both permittivity and permeability are found to be negative in that region. Focussing effect of a flat structure, which is a characteristic feature of a negative index metamaterial, is also confirmed with FDTD caculation.