Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides

We identify a route towards achieving a negative index of refraction at optical frequencies based on coupling between plasmonic waveguides that support backwards waves. We show how modal symmetry can be exploited in metal-dielectric waveguide pairs to achieve negative refraction of both phase and
energy. Control of waveguide coupling yields a metamaterial consisting of a one-dimensional multilayer stack that exhibits an isotropic index of – 1 at a free-space wavelength of 400 nm. The concepts developed here may inspire new low-loss metamaterial designs operating close to the metal plasma frequency.