Electromagnetic origins of negative refraction in coupled plasmonic waveguide metamaterials

Abstract

A metamaterial composed of stacked plasmonic waveguides which support backward propagation along the layers has been shown to exhibit a nearly spherical equifrequency contour (EFC) in which the Floquet-Bloch wave vector ${\mathbf{k}}_{\mathrm{FB}}$ and Poynting vector $\mathbf{S}$ point in opposite directions everywhere on this surface. Experiments performed on this structure have also shown that polarized light beams incident from free space refract to the same side of normal over a wide range of incidence angles. Together, these observations have led researchers to describe this structure as a homogeneous medium with three-dimensionally isotropic negative refractive index; however, a close inspection of the fields throughout the structure as provided in this paper would suggest otherwise. Here, we rigorously analyze the relationship between phase and power flow within the structure by introducing a method to calculate the power flow of all Floquet-Bloch harmonics, information which cannot be obtained from either conventional analysis of EFCs or effective medium theory. Access to power flow of all harmonics enables us to demonstrate the origin of backward power (defined with respect to the direction of ${\mathbf{k}}_{\mathrm{FB}})$, and in doing so, verify the validity of the claimed three-dimensionally isotropic left-handed response and the validity of describing the medium by a simple negative effective index of refraction $n=\ensuremath{-}1$. Knowledge regarding the distribution of power flow across the harmonics can also be used to design highly efficient methods to couple light into and out of these structures. As an example, we show that tailored wave excitation can achieve coupling efficiencies of up to 96%, over 5 times greater than that achieved by normal-incidence plane-wave excitation.