Theory of negative-refractive-index response of double-fishnet structures

A theory is presented of the negative refractive index observed in the so-called double-fishnet structures. We find that the electrical response of these structures is dominated by the cutoff frequency of the hole waveguide whereas the resonant magnetic response is due to the excitation of gap surface plasmon polaritons propagating along the dielectric slab. Associated with this origin, we show how the negative refractive index in these metamaterials presents strong dispersion with the parallel momentum of the incident light.